Communications on Pure and Applied Mathematics最新文献

{"title":"On minimizers in the liquid drop model","authors":"Otis Chodosh,&nbsp;Ian Ruohoniemi","doi":"10.1002/cpa.22229","DOIUrl":"10.1002/cpa.22229","url":null,"abstract":"<p>We prove that round balls of volume <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$le 1$</annotation>\u0000 </semantics></math> uniquely minimize in Gamow's liquid drop model.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"366-381"},"PeriodicalIF":3.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates","authors":"Yu Deng,&nbsp;Alexandru D. Ionescu,&nbsp;Fabio Pusateri","doi":"10.1002/cpa.22224","DOIUrl":"10.1002/cpa.22224","url":null,"abstract":"&lt;p&gt;Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV-type equations. However, our situation here is different since the water waves equations are quasilinear and solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue. We investigate solutions of the gravity water waves system in two dimensions. In the irrotational case, this system can be reduced to an evolution equation on the one-dimensional interface, which is a large torus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${mathbb {T}}_R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of size &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Rge 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Our first main result is a deterministic energy inequality, which provides control of (possibly large) Sobolev norms of solutions for long times, under the condition that a certain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-type norm is small. This energy inequality is of “quintic” type: if the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; norm is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$O(varepsilon)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then the increment of the high-order energies is controlled for times of the order &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$varepsilon ^{-3}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, consistent with the approximate quartic integrability of the system. In the second paper in this sequence, we","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"211-322"},"PeriodicalIF":3.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142170872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence to the planar interface for a nonlocal free-boundary evolution","authors":"Felix Otto,&nbsp;Richard Schubert,&nbsp;Maria G. Westdickenberg","doi":"10.1002/cpa.22225","DOIUrl":"10.1002/cpa.22225","url":null,"abstract":"<p>We capture optimal decay for the Mullins–Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient space dimension three. Far from assuming small or well-prepared initial data, we allow for initial interfaces that do not have graph structure and are not connected, hence explicitly including the regime of Ostwald ripening. In terms only of initially finite (not small) excess mass and excess surface energy, we establish that the surface becomes a Lipschitz graph within a fixed timescale (quantitatively estimated) and remains trapped within this setting. To obtain the graph structure, we leverage regularity results from geometric measure theory. At the same time, we extend a duality method previously employed for one-dimensional PDE problems to higher dimensional, nonlocal geometric evolutions. Optimal algebraic decay rates of excess energy, dissipation, and graph height are obtained.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"161-208"},"PeriodicalIF":3.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotics of block Toeplitz determinants with piecewise continuous symbols","authors":"Estelle Basor,&nbsp;Torsten Ehrhardt,&nbsp;Jani A. Virtanen","doi":"10.1002/cpa.22223","DOIUrl":"10.1002/cpa.22223","url":null,"abstract":"<p>We determine the asymptotics of the block Toeplitz determinants <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>det</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ϕ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$det T_n(phi)$</annotation>\u0000 </semantics></math> as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$Ntimes N$</annotation>\u0000 </semantics></math> matrix-valued piecewise continuous functions <span></span><math>\u0000 <semantics>\u0000 <mi>ϕ</mi>\u0000 <annotation>$phi$</annotation>\u0000 </semantics></math> with a finitely many jumps under mild additional conditions. In particular, we prove that\u0000\u0000 </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"120-160"},"PeriodicalIF":3.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22223","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142090102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tight Lipschitz hardness for optimizing mean field spin glasses","authors":"Brice Huang,&nbsp;Mark Sellke","doi":"10.1002/cpa.22222","DOIUrl":"https://doi.org/10.1002/cpa.22222","url":null,"abstract":"&lt;p&gt;We study the problem of algorithmically optimizing the Hamiltonian &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$H_N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a spherical or Ising mixed &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-spin glass. The maximum asymptotic value &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;OPT&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {OPT}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H_N/N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is characterized by a variational principle known as the Parisi formula, proved first by Talagrand and in more generality by Panchenko. Recently developed approximate message passing (AMP) algorithms efficiently optimize &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H_N/N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; up to a value &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; given by an extended Parisi formula, which minimizes over a larger space of functional order parameters. These two objectives are equal for spin glasses exhibiting a &lt;i&gt;no overlap gap&lt;/i&gt; property (OGP). However, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;OPT&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}&amp;lt; {mathsf {OPT}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can also occur, and no efficient algorithm producing an objective value exceeding &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is known. We prove that for mixed even &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-spin models, no algorithm satisfying an &lt;i&gt;overlap concentration&lt;/i&gt; property can produce an objective larger than &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with non-negligible probability.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"60-119"},"PeriodicalIF":3.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global regularity for critical SQG in bounded domains","authors":"Peter Constantin,&nbsp;Mihaela Ignatova,&nbsp;Quoc-Hung Nguyen","doi":"10.1002/cpa.22221","DOIUrl":"10.1002/cpa.22221","url":null,"abstract":"<p>We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math>. We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"3-59"},"PeriodicalIF":3.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A variational construction of Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities","authors":"Filippo Gaia,&nbsp;Gerard Orriols,&nbsp;Tristan Rivière","doi":"10.1002/cpa.22220","DOIUrl":"https://doi.org/10.1002/cpa.22220","url":null,"abstract":"<p>We construct using variational methods Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities. We obtain these surfaces through a convergence process reminiscent to the Ginzburg–Landau asymptotic analysis in the strongly repulsive regime introduced by Bethuel, Brezis and Hélein. We describe in particular how the prescription of Schoen–Wolfson conical singularities is related to optimal Wente constants.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 12","pages":"4390-4431"},"PeriodicalIF":3.1,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost sharp lower bound for the nodal volume of harmonic functions","authors":"Alexander Logunov,&nbsp;Lakshmi Priya M. E.,&nbsp;Andrea Sartori","doi":"10.1002/cpa.22207","DOIUrl":"10.1002/cpa.22207","url":null,"abstract":"<p>This paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let <span></span><math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math> be a real-valued harmonic function in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$u(0)=0$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$nge 3$</annotation>\u0000 </semantics></math>. We prove\u0000\u0000 </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 12","pages":"4328-4389"},"PeriodicalIF":3.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141177297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Allen–Cahn solutions with triple junction structure at infinity","authors":"Étienne Sandier,&nbsp;Peter Sternberg","doi":"10.1002/cpa.22204","DOIUrl":"10.1002/cpa.22204","url":null,"abstract":"<p>We construct an entire solution <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$U:mathbb {R}^2rightarrow mathbb {R}^2$</annotation>\u0000 </semantics></math> to the elliptic system\u0000\u0000 </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 11","pages":"4163-4211"},"PeriodicalIF":3.1,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140953873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicative chaos measures from thick points of log-correlated fields","authors":"Janne Junnila,&nbsp;Gaultier Lambert,&nbsp;Christian Webb","doi":"10.1002/cpa.22205","DOIUrl":"10.1002/cpa.22205","url":null,"abstract":"<p>We prove that multiplicative chaos measures can be constructed from extreme level sets or <i>thick points</i> of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of suitable exponential moments for the field. As an application, we establish that these estimates hold for the logarithm of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix (CUE), using known asymptotics for Toeplitz determinant with (merging) Fisher–Hartwig singularities. Hence, this proves a conjecture of Fyodorov and Keating concerning the fluctuations of the volume of thick points of the CUE characteristic polynomial.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 11","pages":"4212-4286"},"PeriodicalIF":3.1,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22205","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140954009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}