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Effective Discreteness Radius of Stabilizers for Stationary Actions 稳定作用下稳定器的有效离散半径
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-03-22 DOI: 10.1307/mmj/20217209
T. Gelander, Arie Levit, G. Margulis
{"title":"Effective Discreteness Radius of Stabilizers for Stationary Actions","authors":"T. Gelander, Arie Levit, G. Margulis","doi":"10.1307/mmj/20217209","DOIUrl":"https://doi.org/10.1307/mmj/20217209","url":null,"abstract":"We prove an effective variant of the Kazhdan-Margulis theorem generalized to stationary actions of semisimple groups over local fields: the probability that the stabilizer of a random point admits a non-trivial intersection with a small $r$-neighborhood of the identity is at most $beta r^delta$ for some explicit constants $beta, delta>0$ depending only the group. This is a consequence of a key convolution inequality. We deduce that vanishing at infinity of injectivity radius implies finiteness of volume. Further applications are the compactness of the space of discrete stationary random subgroups and a novel proof of the fact that all lattices in semisimple groups are weakly cocompact.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"5 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88688339","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: 2
Extremizers and Stability of the Betke–Weil Inequality Betke-Weil不等式的极值型与稳定性
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-03-22 DOI: 10.1307/mmj/20216063
F. Bartha, Ferenc Bencs, K. Boroczky, D. Hug
{"title":"Extremizers and Stability of the Betke–Weil Inequality","authors":"F. Bartha, Ferenc Bencs, K. Boroczky, D. Hug","doi":"10.1307/mmj/20216063","DOIUrl":"https://doi.org/10.1307/mmj/20216063","url":null,"abstract":"Let K be a compact convex domain in the Euclidean plane. The mixed area A(K,−K) of K and−K can be bounded from above by 1/(6 √ 3)L(K)2, where L(K) is the perimeter of K. This was proved by Ulrich Betke and Wolfgang Weil (1991). They also showed that if K is a polygon, then equality holds if and only if K is a regular triangle. We prove that among all convex domains, equality holds only in this case, as conjectured by Betke and Weil. This is achieved by establishing a stronger stability result for the geometric inequality 6 √ 3A(K,−K) ≤ L(K)2.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76577628","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: 1
A Generalization of Pisier Homogeneous Banach Algebra Pisier齐次Banach代数的推广
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-03-17 DOI: 10.1307/mmj/20205914
Safari Mukeru
{"title":"A Generalization of Pisier Homogeneous Banach Algebra","authors":"Safari Mukeru","doi":"10.1307/mmj/20205914","DOIUrl":"https://doi.org/10.1307/mmj/20205914","url":null,"abstract":"In 1979 Pisier proved remarkably that a sequence of independent and identically distributed standard Gaussian random variables determines, via random Fourier series, a homogeneous Banach algebra P strictly contained in C(T), the class of continuous functions on the unit circle T and strictly containing the classical Wiener algebra A(T), that is, A(T) $ P $ C(T). This improved some previous results obtained by Zafran in solving a long-standing problem raised by Katznelson. In this paper we extend Pisier’s result by showing that any probability measure on the unit circle defines a homogeneous Banach algebra contained in C(T). Thus Pisier algebra is not an isolated object but rather an element in a large class of Pisier-type algebras. We consider the case of spectral measures of stationary sequences of Gaussian random variables and obtain a sufficient condition for the boundedness of the random Fourier series ∑ n∈Z f̂(n) ξn exp(2πint) in the general setting of dependent random variables (ξn).","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"88 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74036838","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: 2
When Is a Reductive Group Scheme Linear? 约化群方案何时是线性的?
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-03-12 DOI: 10.1307/mmj/20217208
P. Gille
{"title":"When Is a Reductive Group Scheme Linear?","authors":"P. Gille","doi":"10.1307/mmj/20217208","DOIUrl":"https://doi.org/10.1307/mmj/20217208","url":null,"abstract":"We show that a reductive group scheme over a base scheme S admits a faithful linear representation if and only if its radical torus is isotrivial, that is, it splits after a finite {'e}tale cover.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"67 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73392976","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: 8
On the Conditional Measures on the Orbits of the Complex Torus 关于复环面轨道的条件测度
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-02-17 DOI: 10.1307/mmj/20216050
Szymon Myga
{"title":"On the Conditional Measures on the Orbits of the Complex Torus","authors":"Szymon Myga","doi":"10.1307/mmj/20216050","DOIUrl":"https://doi.org/10.1307/mmj/20216050","url":null,"abstract":"We explore the structure of invariant measures on compact Kähler manifolds with Hamiltonian torus actions. We derive the formula for conditional measures on the orbits of the complex torus and use it to prove a conditional statement about uniqueness of solutions to the g-Monge-Ampère equation.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"65 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75809965","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
Homomorphisms of Algebraic Groups: Representability and Rigidity 代数群的同态:可表示性与刚性
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-29 DOI: 10.1307/mmj/20217214
M. Brion
{"title":"Homomorphisms of Algebraic Groups: Representability and Rigidity","authors":"M. Brion","doi":"10.1307/mmj/20217214","DOIUrl":"https://doi.org/10.1307/mmj/20217214","url":null,"abstract":"Given two algebraic groups G, H over a field k, we investigate the representability of the functor of morphisms (of schemes) Hom(G,H) and the subfunctor of homomorphisms (of algebraic groups)Homgp(G,H). We show thatHom(G,H) is represented by a group scheme, locally of finite type, if the k-vector space O(G) is finite-dimensional; the converse holds if H is not étale. When G is linearly reductive and H is smooth, we show that Homgp(G,H) is represented by a smooth scheme M ; moreover, every orbit of H acting by conjugation on M is open.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87496277","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: 9
How Far Are p-Adic Lie Groups from Algebraic Groups? p-进李群离代数群有多远?
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-26 DOI: 10.1307/mmj/20217205
Y. Benoist, Jean-François Quint
{"title":"How Far Are p-Adic Lie Groups from Algebraic Groups?","authors":"Y. Benoist, Jean-François Quint","doi":"10.1307/mmj/20217205","DOIUrl":"https://doi.org/10.1307/mmj/20217205","url":null,"abstract":"We show that, in a weakly regular p-adic Lie group G, the subgroup Gu spanned by the one-parameter subgroups of G admits a Levi decomposition. As a consequence, there exists a regular open subgroup of G which contains Gu","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"24 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80780462","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: 1
Limit Groups over Coherent Right-Angled Artin Groups Are Cyclic Subgroup Separable 相干直角Artin群上的极限群是循环子群可分的
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-25 DOI: 10.1307/mmj/20216031
J. Fruchter
{"title":"Limit Groups over Coherent Right-Angled Artin Groups Are Cyclic Subgroup Separable","authors":"J. Fruchter","doi":"10.1307/mmj/20216031","DOIUrl":"https://doi.org/10.1307/mmj/20216031","url":null,"abstract":"We prove that cyclic subgroup separability is preserved under exponential completion for groups that belong to a class that includes all coherent RAAGs and toral relatively hyperbolic groups; we do so by exploiting the structure of these completions as iterated free products with commuting subgroups. From this we deduce that the cyclic subgroups of limit groups over coherent RAAGs are separable, answering a question of Casals-Ruiz, Duncan and Kazachov. We also discuss relations between free products with commuting subgroups and the word problem, and recover the fact that limit groups over coherent RAAGs and toral relatively hyperbolic groups have a solvable word problem.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73483973","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: 1
Khovanskii-Finite Rational Curves of Arithmetic Genus 2 khovanski -算术格2的有限有理曲线
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-23 DOI: 10.1307/mmj/20216048
N. Ilten, Ahmad Mokhtar
{"title":"Khovanskii-Finite Rational Curves of Arithmetic Genus 2","authors":"N. Ilten, Ahmad Mokhtar","doi":"10.1307/mmj/20216048","DOIUrl":"https://doi.org/10.1307/mmj/20216048","url":null,"abstract":"We study the existence of Khovanskii-finite valuations for rational curves of arithmetic genus two. We provide a semi-explicit description of the locus of degree n+ 2 rational curves in Pn of arithmetic genus two that admit a Khovanskii-finite valuation. Furthermore, we describe an effective method for determining if a rational curve of arithmetic genus two defined over a number field admits a Khovanskii-finite valuation. This provides a criterion for deciding if such curves admit a toric degeneration. Finally, we show that rational curves with a single unibranch singularity are always Khovanskii-finite if their arithmetic genus is sufficiently small.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"182 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80345974","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
Big Mapping Class Groups and the Co-Hopfian Property 大映射类群与共合性
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-01-18 DOI: 10.1307/mmj/20216075
J. Aramayona, C. Leininger, A. McLeay
{"title":"Big Mapping Class Groups and the Co-Hopfian Property","authors":"J. Aramayona, C. Leininger, A. McLeay","doi":"10.1307/mmj/20216075","DOIUrl":"https://doi.org/10.1307/mmj/20216075","url":null,"abstract":"We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pure) mapping class groups are not co-Hopfian; these are the first examples of injective endomorphisms of mapping class groups (of surfaces with empty boundary) that fail to be surjective. We then prove that, subject to some topological conditions on the domain surface, any continuous injective homomorphism between (arbitrary) big mapping class groups that sends Dehn twists to Dehn twists is induced by homeomorphism. Finally, we explore the extent to which, in stark contrast to the finite-type case, superinjective maps between curve graphs impose no topological restrictions on the underlying surfaces.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":"47 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77170291","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: 1
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