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Nonlinear Rough Fokker–Planck Equations 非线性粗糙Fokker-Planck方程
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-11-05 DOI: 10.1007/s11040-026-09590-y
Fabio Bugini, Peter K. Friz, Wilhelm Stannat
{"title":"Nonlinear Rough Fokker–Planck Equations","authors":"Fabio Bugini,&nbsp;Peter K. Friz,&nbsp;Wilhelm Stannat","doi":"10.1007/s11040-026-09590-y","DOIUrl":"10.1007/s11040-026-09590-y","url":null,"abstract":"<div><p>McKean–Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker–Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and conditional law dependence, the evolution becomes random and is governed by a stochastic Fokker–Planck equation; that is, a nonlinear, nonlocal SPDE in the space of measures. (Such equations constitute an important ingredient in the theory of mean-field games with common noise.) Well-posedness of such SPDEs is a difficult problem, the best result to date due to Coghi–Gess [5], which however comes with dimension-dependent regularity assumptions. In the present work, we show how rough path techniques can circumvent these entirely. Hence, and somewhat contrarily to common belief, the use of rough paths leads to substantially less regularity demands on the coefficients than methods rooted in classical stochastic analysis methods.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09590-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hamiltonians, Their Newton Polygons and Painlevé Equations 哈密顿人，他们的牛顿多边形和painlevleve方程
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-30 DOI: 10.1007/s11040-026-09598-4
Galina Filipuk
{"title":"Hamiltonians, Their Newton Polygons and Painlevé Equations","authors":"Galina Filipuk","doi":"10.1007/s11040-026-09598-4","DOIUrl":"10.1007/s11040-026-09598-4","url":null,"abstract":"<div><p>We study selected cases of the Hamiltonian of bi-degree (3, 2) with arbitrary analytic coefficients. By imposing constraints on the coefficient functions, which can lower the bi-degree, we can recover the well-known polynomial Hamiltonians with rational coefficients for the Painlevé equations in the regularisation of the corresponding Hamiltonian system. Moreover, for the first and the second Painlevé equations we can also recover polynomial Hamiltonians with meromorphic coefficients. In addition, we examine various shapes of the Newton polygons and graphically visualize the coalescence of the Painlevé equations via inclusion of the Newton polygons into each other.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09598-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lieb–Robinson Bounds, Automorphic Equivalence and LPPL for Long-Range Interacting Fermions 远距离相互作用费米子的Lieb-Robinson边界、自同构等价和LPPL
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-27 DOI: 10.1007/s11040-026-09584-w
Stefan Teufel, Tom Wessel
{"title":"Lieb–Robinson Bounds, Automorphic Equivalence and LPPL for Long-Range Interacting Fermions","authors":"Stefan Teufel,&nbsp;Tom Wessel","doi":"10.1007/s11040-026-09584-w","DOIUrl":"10.1007/s11040-026-09584-w","url":null,"abstract":"<div><p>We prove a Lieb–Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local perturbations perturb locally (LPPL) principle for these systems. The proof of the Lieb–Robinson bound is based on the work of Else et al. [5], and our results also apply to spin systems. We explain why some newer Lieb–Robinson bounds for long-range spin systems cannot be used to prove the locality of the quasi-local inverse Liouvillian, and in some cases may not even hold for fermionic systems.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09584-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kovalevskaya Exponents of the Riccati Hierarchy Riccati层次的Kovalevskaya指数
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-20 DOI: 10.1007/s11040-026-09597-5
Changyu Zhou
{"title":"Kovalevskaya Exponents of the Riccati Hierarchy","authors":"Changyu Zhou","doi":"10.1007/s11040-026-09597-5","DOIUrl":"10.1007/s11040-026-09597-5","url":null,"abstract":"<div><p>We carry out a Kovalevskaya analysis of the Riccati hierarchy. We determine all indicial loci and Kovalevskaya exponents and identify a rigid recursive structure governing how free parameters enter Laurent solutions. We further identify a nontrivial quasi-homogeneous vector field commuting with the hierarchy and use it to obtain an explicit parametrization of all solutions in terms of a single polynomial. Notably, in the two-dimensional case, the same general solution is recovered by the blow-up resolution. Within this parametrization, collisions of poles correspond to degeneration limits of the principal Laurent family, through which lower indicial loci appear. Finally, negative Kovalevskaya exponents are interpreted analytically through annular Laurent expansions, which describe how different collections of poles dominate in different complex regions.\u0000</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Condensation in Stochastic Lattice Gases with Size-Dependent Stationary Weights 具有定权大小的随机点阵气体的缩聚
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-17 DOI: 10.1007/s11040-026-09594-8
Joshua Blank, Paul Chleboun, Stefan Grosskinsky, Watthanan Jatuviriyapornchai
{"title":"Condensation in Stochastic Lattice Gases with Size-Dependent Stationary Weights","authors":"Joshua Blank,&nbsp;Paul Chleboun,&nbsp;Stefan Grosskinsky,&nbsp;Watthanan Jatuviriyapornchai","doi":"10.1007/s11040-026-09594-8","DOIUrl":"10.1007/s11040-026-09594-8","url":null,"abstract":"<div><p>We consider stochastic lattice gases with stationary product weights and a polynomial perturbation vanishing with the system size that leads to condensation. If the density of particles exceeds a critical value the system phase separates into a bulk with homogeneous distribution of particles and a condensed phase. Depending on parameter values, the latter consists of a single macroscopic cluster or a diverging number of independent clusters on a smaller scale. We establish the condensation transition via the equivalence of ensembles and the main novelty is a derivation of the cluster size distribution using size-biased sampling, generalizing previous work on zero-range and inclusion processes. Simulations of zero-range processes illustrate our theoretical results on the condensate scale and size distribution.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Degenerations of the Fourth Order q-Garnier System Arising from Confluences in Quivers 颤振中汇聚引起的四阶q-Garnier系统的退化
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-16 DOI: 10.1007/s11040-026-09595-7
Kazuya Matsugashita, Takao Suzuki, Satoshi Tsuchimi
{"title":"Degenerations of the Fourth Order q-Garnier System Arising from Confluences in Quivers","authors":"Kazuya Matsugashita,&nbsp;Takao Suzuki,&nbsp;Satoshi Tsuchimi","doi":"10.1007/s11040-026-09595-7","DOIUrl":"10.1007/s11040-026-09595-7","url":null,"abstract":"<div><p>The <i>q</i>-Garnier system was first proposed by Sakai, and alternative directions for its discrete time evolutions were provided by Nagao and Yamada. Recently, it was shown that all of those evolution directions are derived from a birational representation of an extended affine Weyl group which arises from the cluster algebraic construction established by Masuda, Okubo and Tsuda. In this article, we investigate a degeneration structure of the fourth order <i>q</i>-Garnier system by using confluences in quivers.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Connection Problem of q-linear Equations and the q-Painlevé Third Equation q-线性方程与q- painlelevel3方程的连接问题
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-05 DOI: 10.1007/s11040-026-09593-9
Yousuke Ohyama
{"title":"Connection Problem of q-linear Equations and the q-Painlevé Third Equation","authors":"Yousuke Ohyama","doi":"10.1007/s11040-026-09593-9","DOIUrl":"10.1007/s11040-026-09593-9","url":null,"abstract":"<div><p>We study the analytic properties of solutions to the <i>q</i>-Painlevé third equation. The <i>q</i>-Painlevé third equation can be represented as a connection preserving deformation of a linear <i>q</i>-difference equation. We investigate the connection problem for this linear <i>q</i>-difference equation and show that the connection matrix is expressed as a product of connection matrices arising from confluent <i>q</i>-hypergeometric equations.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Stability for F-Yang-Mills Functional on (mathbb {C}P^n) F-Yang-Mills泛函的稳定性 (mathbb {C}P^n)
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-09-24 DOI: 10.1007/s11040-026-09592-w
Yang Wen
{"title":"The Stability for F-Yang-Mills Functional on (mathbb {C}P^n)","authors":"Yang Wen","doi":"10.1007/s11040-026-09592-w","DOIUrl":"10.1007/s11040-026-09592-w","url":null,"abstract":"<div><p>In this paper, we study the critical points of <i>F</i>-Yang-Mills functional on <span>(mathbb {C}P^n)</span>, which are called <i>F</i>-Yang-Mills connections, which is a generalization of Yang-Mills connections. We prove that if <span>((2+frac{2}{n})F''(x)x+(n+1)F'(x)&lt;0)</span>, then the weakly stable <i>F</i>-Yang-Mills connection on <span>(mathbb {C}P^n)</span> must be flat. Moreover, if <span>((2+frac{2}{n})F''(x)x+(n+1)F'(x)=0)</span>, we obtain the structure of curvatures corresponding to weakly stable connections. We also show a gap theorem for <i>F</i>-Yang-Mills connections on <span>(mathbb {C}P^n)</span>. Our approach is inspired by Bourguignon and Lawson’s study of Yang-Mills stability on spheres.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Markov Chains for an Asymmetric Mixed Ising–XY Model on a Cayley Tree Cayley树上不对称混合isingxy模型的量子Markov链
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-09-22 DOI: 10.1007/s11040-026-09591-x
Farrukh Mukhamedov
{"title":"Quantum Markov Chains for an Asymmetric Mixed Ising–XY Model on a Cayley Tree","authors":"Farrukh Mukhamedov","doi":"10.1007/s11040-026-09591-x","DOIUrl":"10.1007/s11040-026-09591-x","url":null,"abstract":"<div><p>We study a mixed quantum Ising–<i>XY</i> model on the semi-infinite rooted Cayley tree of order two. For every vertex <i>u</i>, the edge <span>(langle u,(u,1)rangle )</span> carries an <i>XY</i> interaction and the edge <span>(langle u,(u,2)rangle )</span> carries an Ising interaction. Using the compatibility criterion for tree-indexed quantum Markov chains and consistently working with the normalized trace, we derive the translation-invariant boundary equation and compute explicitly the associated local transfer operator, namely the one-step partial-trace map which propagates successor boundary data to the parent vertex. We prove that the boundary equation has a unique positive translation-invariant solution for all <span>(J_I,J_{XY}in mathbb {R})</span> and <span>(beta &gt;0)</span>. Hence the model admits a unique translation-invariant quantum Markov chain generated by a positive translation-invariant boundary condition. We also show that the reduced boundary-law dynamics, i.e. the induced finite-dimensional recursion for the boundary-law parameters, has no admissible periodic points of period greater than one and compute the local two-site entanglement on the natural three-site cluster of the tree.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149014575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Polynomial Poisson Algebras and Superintegrable Systems from Cartan Centralisers of Types (B_3), (C_3) and (D_3) 多项式泊松代数和来自(B_3), (C_3)和类型Cartan中心的超可积系统 (D_3)
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-09-07 DOI: 10.1007/s11040-026-09589-5
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette, Junze Zhang, Yao-Zhong Zhang
{"title":"Polynomial Poisson Algebras and Superintegrable Systems from Cartan Centralisers of Types (B_3), (C_3) and (D_3)","authors":"Rutwig Campoamor-Stursberg,&nbsp;Danilo Latini,&nbsp;Ian Marquette,&nbsp;Junze Zhang,&nbsp;Yao-Zhong Zhang","doi":"10.1007/s11040-026-09589-5","DOIUrl":"10.1007/s11040-026-09589-5","url":null,"abstract":"<div><p>In this work, we develop a root system construction for Cartan centralisers of classical complex semisimple Lie algebras of types <i>B</i>, <i>C</i> and <i>D</i>, and we analyse the associated polynomial Poisson algebras completely and explicitly in the rank-three cases <span>(B_3)</span>, <span>(C_3)</span>, and <span>(D_3)</span>. This rank 3 case is already highly non-trivial. For <span>(B_n)</span>, <span>(C_n)</span> and <span>(D_n)</span>, we use this new method to present the main division of cases and how the indecomposable polynomials organize into different types that can be understood via the root systems and their properties. An explicit description of all indecomposable polynomials of type <span>(B_n)</span> is provided only for the rank 3. We provide insight how the type <i>A</i> construction changes once the root system contains signed long roots and, in types <span>(B_n)</span> and <span>(C_n)</span>, short or doubled roots. Thus, the directed-cycle construction for type <span>(A_{n-1})</span> becomes a sign-indexed factor construction with permutation-root, long-root, and short-root generators. We develop the idea of constructing algebraic superintegrable systems and their integrals from the generators of these polynomial Poisson algebras. The resulting finite rank-three sets of generators are used to describe the inclusion relations between the corresponding finitely generated Poisson <span>(mathbb C[mathfrak {h}^*])</span>-algebras and to construct algebraic superintegrable systems attached to the reduction chains <span>(mathfrak {h} subset mathfrak {so}(6,mathbb {C}))</span>, <span>(mathfrak {h} subset mathfrak {so}(7,mathbb {C}))</span>, and <span>(mathfrak {h} subset mathfrak {sp}(6,mathbb {C}))</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09589-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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