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L 2-Maximal Functions on Graded Lie Groups L 2-梯度李群上的最大函数
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-22 DOI: 10.1093/imrn/rnae105
Duván Cardona
{"title":"L 2-Maximal Functions on Graded Lie Groups","authors":"Duván Cardona","doi":"10.1093/imrn/rnae105","DOIUrl":"https://doi.org/10.1093/imrn/rnae105","url":null,"abstract":"Bourgain in his seminal paper of 1986 about the analysis of maximal functions associated to convex bodies has estimated in a sharp way the $L^{2}$-operator norm of the maximal function associated to a kernel $Kin L^{1},$ with differentiable Fourier transform $widehat{K}.$ We formulate the extension to Bourgain’s $L^{2}$-estimate in the setting of maximal functions on graded Lie groups. Our criterion is formulated in terms of the group Fourier transform of the kernel. We discuss the application of our main result to the $L^{p}$-boundedness of maximal functions on graded Lie groups.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Word Measures on Unitary Groups: Improved Bounds for Small Representations 单元群上的词量：小表征的改进界限
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-21 DOI: 10.1093/imrn/rnae100
Yaron Brodsky
{"title":"Word Measures on Unitary Groups: Improved Bounds for Small Representations","authors":"Yaron Brodsky","doi":"10.1093/imrn/rnae100","DOIUrl":"https://doi.org/10.1093/imrn/rnae100","url":null,"abstract":"Let $F$ be a free group of rank $r$ and fix some $win F$. For any compact group $G$ we can define a measure $mu _{w,G}$ on $G$ by (Haar-)uniformly sampling $g_{1},...,g_{r}in G$ and evaluating $w(g_{1},...,g_{r})$. In [23], Magee and Puder study the behavior of the moments of $mu _{w,U(n)}$ as a function of $n$, establishing a connection between their asymptotic behavior and certain algebraic invariants of $w$, such as its commutator length. We employ geometric insights to refine their analysis, and show that the asymptotic behavior of the moments is also governed by the primitivity rank of $w$. Additionally, we also apply our methods to prove a special case of a conjecture of Hanany and Puder [13, Conjecture 1.13] regarding the asymptotic behavior of expected values of irreducible characters of $U(n)$ under $mu _{w,U(n)}$.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Two-Point Polynomial Patterns in Subsets of Positive Density in $mathbb{R}^{n}$ $mathbb{R}^{n}$中正密度子集的两点多项式模式
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-21 DOI: 10.1093/imrn/rnae108
Xuezhi Chen, Changxing Miao
{"title":"Two-Point Polynomial Patterns in Subsets of Positive Density in $mathbb{R}^{n}$","authors":"Xuezhi Chen, Changxing Miao","doi":"10.1093/imrn/rnae108","DOIUrl":"https://doi.org/10.1093/imrn/rnae108","url":null,"abstract":"\u0000 Let $gamma (t)=(P_{1}(t),ldots ,P_{n}(t))$ where $P_{i}$ is a real polynomial with zero constant term for each $1leq ileq n$. We will show the existence of the configuration ${x,x+gamma (t)}$ in sets of positive density $epsilon $ in $[0,1]^{n}$ with a gap estimate $tgeq delta (epsilon )$ when $P_{i}$’s are arbitrary, and in $[0,N]^{n}$ with a gap estimate $tgeq delta (epsilon )N^{n}$ when $P_{i}$’s are of distinct degrees where $delta (epsilon )=exp left (-exp left (cepsilon ^{-4}right )right )$ and $c$ only depends on $gamma $. To prove these two results, decay estimates of certain oscillatory integral operators and Bourgain’s reduction are primarily utilised. For the first result, dimension-reducing arguments are also required to handle the linear dependency. For the second one, we will prove a stronger result instead, since then an anisotropic rescaling is allowed in the proof to eliminate the dependence of the decay estimate on $N$. And as a byproduct, using the strategy token to prove the latter case, we extend the corner-type Roth theorem previously proven by the first author and Guo.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On the Weak Local Arthur Packets Conjecture for Split Classical Groups 论分裂经典群的弱局部阿瑟包猜想
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-17 DOI: 10.1093/imrn/rnae098
Baiying Liu, Chi-Heng Lo
{"title":"On the Weak Local Arthur Packets Conjecture for Split Classical Groups","authors":"Baiying Liu, Chi-Heng Lo","doi":"10.1093/imrn/rnae098","DOIUrl":"https://doi.org/10.1093/imrn/rnae098","url":null,"abstract":"\u0000 Recently, motivated by the theory of real local Arthur packets, making use of the wavefront sets of representations over non-Archimedean local fields $F$, Ciubotaru, Mason-Brown, and Okada defined the weak local Arthur packets consisting of certain unipotent representations and conjectured that they are unions of local Arthur packets. In this paper, we prove this conjecture for $textrm{Sp}_{2n}(F)$ and split $textrm{SO}_{2n+1}(F)$ with the assumption of the residue field characteristic of $F$ being large. In particular, this implies the unitarity of these unipotent representations. We also discuss the generalization of the weak local Arthur packets beyond unipotent representations, which reveals the close connection with a conjecture of Jiang on the structure of wavefront sets for representations in local Arthur packets.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141126640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Wasserstein Distance for Ricci Shrinkers 利玛窦收缩器的瓦瑟斯坦距离
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-15 DOI: 10.1093/imrn/rnae099
Franciele Conrado, Detang Zhou
{"title":"The Wasserstein Distance for Ricci Shrinkers","authors":"Franciele Conrado, Detang Zhou","doi":"10.1093/imrn/rnae099","DOIUrl":"https://doi.org/10.1093/imrn/rnae099","url":null,"abstract":"Let $(M^{n},g,f)$ be a Ricci shrinker such that $text{Ric}_{f}=frac{1}{2}g$ and the measure induced by the weighted volume element $(4pi )^{-frac{n}{2}}e^{-f}dv_{g}$ is a probability measure. Given a point $pin M$, we consider two probability measures defined in the tangent space $T_{p}M$, namely the Gaussian measure $gamma $ and the measure $overline{nu }$ induced by the exponential map of $M$ to $p$. In this paper, we prove a result that provides an upper estimate for the Wasserstein distance with respect to the Euclidean metric $g_{0}$ between the measures $overline{nu }$ and $gamma $, and which also elucidates the rigidity implications resulting from this estimate.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Equivariant Cohomology and Conditional Oriented Matroids 等价同调与条件定向矩阵
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-14 DOI: 10.1093/imrn/rnad025
Galen Dorpalen-Barry, Nicholas Proudfoot, Jidong Wang
{"title":"Equivariant Cohomology and Conditional Oriented Matroids","authors":"Galen Dorpalen-Barry, Nicholas Proudfoot, Jidong Wang","doi":"10.1093/imrn/rnad025","DOIUrl":"https://doi.org/10.1093/imrn/rnad025","url":null,"abstract":"We give a cohomological interpretation of the Heaviside filtration on the Varchenko–Gelfand ring of a pair $({mathcal{A}},{mathcal{K}})$, where ${mathcal{A}}$ is a real hyperplane arrangement and ${mathcal{K}}$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where ${mathcal{K}}$ is the ambient vector space. We also define the Gelfand–Rybnikov ring of a conditional oriented matroid, which simultaneously generalizes the Gelfand–Rybnikov ring of an oriented matroid and the aforementioned Varchenko–Gelfand ring of a pair. We give purely combinatorial presentations of the ring, its associated graded, and its Rees algebra.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Annihilating Branching Brownian Motion 湮没分支布朗运动
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-09 DOI: 10.1093/imrn/rnae068
Daniel Ahlberg, Omer Angel, Brett Kolesnik
{"title":"Annihilating Branching Brownian Motion","authors":"Daniel Ahlberg, Omer Angel, Brett Kolesnik","doi":"10.1093/imrn/rnae068","DOIUrl":"https://doi.org/10.1093/imrn/rnae068","url":null,"abstract":"We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Correction to: The Stability of Relativistic Fluids in Linearly Expanding Cosmologies 更正：线性膨胀宇宙中相对论流体的稳定性
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-08 DOI: 10.1093/imrn/rnae102
{"title":"Correction to: The Stability of Relativistic Fluids in Linearly Expanding Cosmologies","authors":"","doi":"10.1093/imrn/rnae102","DOIUrl":"https://doi.org/10.1093/imrn/rnae102","url":null,"abstract":"","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141000942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Induced Subgraph Density. I. A loglog Step Towards Erd̋s–Hajnal 诱导子图密度。I. 迈向 Erd̋s-Hajnal 的日志步骤
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-07 DOI: 10.1093/imrn/rnae065
Matija Bucić, Tung Nguyen, Alex Scott, Paul Seymour
{"title":"Induced Subgraph Density. I. A loglog Step Towards Erd̋s–Hajnal","authors":"Matija Bucić, Tung Nguyen, Alex Scott, Paul Seymour","doi":"10.1093/imrn/rnae065","DOIUrl":"https://doi.org/10.1093/imrn/rnae065","url":null,"abstract":"In 1977, Erd̋s and Hajnal made the conjecture that, for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^{c}$, and they proved that this is true with $ |G|^{c}$ replaced by $2^{csqrt{log |G|}}$. Until now, there has been no improvement on this result (for general $H$). We prove a strengthening: that for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ with $|G|ge 2$ has a clique or stable set of size at least $$ begin{align*} &2^{csqrt{log |G|loglog|G|}}.end{align*} $$ Indeed, we prove the corresponding strengthening of a theorem of Fox and Sudakov, which in turn was a common strengthening of theorems of Rödl, Nikiforov, and the theorem of Erd̋s and Hajnal mentioned above.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Arthur Packets for Quasisplit GSp(2n) and GO(2n) Over a p-Adic Field p 阿基米德域上的 Quasisplit GSp(2n) 和 GO(2n) 的亚瑟数据包
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-07 DOI: 10.1093/imrn/rnae086
Bin Xu
{"title":"Arthur Packets for Quasisplit GSp(2n) and GO(2n) Over a p-Adic Field","authors":"Bin Xu","doi":"10.1093/imrn/rnae086","DOIUrl":"https://doi.org/10.1093/imrn/rnae086","url":null,"abstract":"We construct the Arthur packets for symplectic and even orthogonal similitude groups over a $p$-adic field and show that they are stable and satisfy the twisted endoscopic character relations.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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