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Kyoto Journal of Mathematics最新文献

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Subexponential densities of compound Poisson sums and the supremum of a random walk 复合Poisson和的次指数密度与随机游动的上确界
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2020-01-29 DOI: 10.1215/21562261-2022-0041
Takaaki Shimura, Toshiro Watanabe
{"title":"Subexponential densities of compound Poisson sums and the supremum of a random walk","authors":"Takaaki Shimura, Toshiro Watanabe","doi":"10.1215/21562261-2022-0041","DOIUrl":"https://doi.org/10.1215/21562261-2022-0041","url":null,"abstract":"We characterize the subexponential densities on $(0,infty)$ for compound Poisson distributions on $[0,infty)$ with absolutely continuous Levy measures. As a corollary, we show that the class of all subexponential probability density functions on $mathbb R_+$ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on $(0,infty)$ for the distribution of the supremum of a random walk.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41663824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
Averaging principles for mixed fast-slow systems driven by fractional Brownian motion 分数布朗运动驱动的混合快慢系统的平均原理
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2020-01-20 DOI: 10.1215/21562261-2023-0001
B. Pei, Y. Inahama, Yong Xu
{"title":"Averaging principles for mixed fast-slow systems driven by fractional Brownian motion","authors":"B. Pei, Y. Inahama, Yong Xu","doi":"10.1215/21562261-2023-0001","DOIUrl":"https://doi.org/10.1215/21562261-2023-0001","url":null,"abstract":"We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes integral using the tools of fractional calculus. An averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a noise to be averaged out in the limit is established. It is shown that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. The implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 15
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras 简单表面奇异点Hilbert格式的欧拉数与量子仿射代数标准模的量子维数
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2020-01-12 DOI: 10.1215/21562261-2021-0006
H. Nakajima
{"title":"Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras","authors":"H. Nakajima","doi":"10.1215/21562261-2021-0006","DOIUrl":"https://doi.org/10.1215/21562261-2021-0006","url":null,"abstract":"We prove the conjecture by Gyenge, Nemethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of points $operatorname{Hilb}^n(mathbb C^2/Gamma)$ on a simple singularity $mathbb C^2/Gamma$, where $Gamma$ is a finite subgroup of $mathrm{SL}(2)$. We deduce it from the claim that quantum dimensions of standard modules for the quantum affine algebra associated with $Gamma$ at $zeta = exp(frac{2pi i}{2(h^vee+1)})$ are always $1$, which is a special case of a conjecture by Kuniba [Kun93]. Here $h^vee$ is the dual Coxeter number. We also prove the claim, which was not known for $E_7$, $E_8$ before.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42371611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Quasi-Lie bialgebras of loops in quasisurfaces 准曲面上环的拟李双代数
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2020-01-07 DOI: 10.1215/21562261-2022-0034
V. Turaev
{"title":"Quasi-Lie bialgebras of loops in quasisurfaces","authors":"V. Turaev","doi":"10.1215/21562261-2022-0034","DOIUrl":"https://doi.org/10.1215/21562261-2022-0034","url":null,"abstract":"We discuss natural operations on loops in a quasi-surface and show that these operations define a structure of a quasi-Lie bialgebra in the module generated by the set of free homotopy classes of non-contractible loops.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48031619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Semigroups in 3-graded Lie groups and endomorphisms of standard subspaces 3阶李群中的半群与标准子空间的自同态
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-12-31 DOI: 10.1215/21562261-2022-0017
K. Neeb
{"title":"Semigroups in 3-graded Lie groups and endomorphisms of standard subspaces","authors":"K. Neeb","doi":"10.1215/21562261-2022-0017","DOIUrl":"https://doi.org/10.1215/21562261-2022-0017","url":null,"abstract":"Let V be a standard subspace in the complex Hilbert space H and U : G to U(H) be a unitary representation of a finite dimensional Lie group. We assume the existence of an element h in the Lie algebra of G such that U(exp th) is the modular group of V and that the modular involution J_V normalizes U(G). We want to determine the semigroup $S_V = { gin G : U(g)V subseteq V}.$ In previous work we have seen that its infinitesimal generators span a Lie algebra on which ad h defines a 3-grading, and here we completely determine the semigroup S_V under the assumption that ad h defines a 3-grading. Concretely, we show that the ad h-eigenspaces for the eigenvalue $pm 1$ contain closed convex cones $C_pm$, such that $S_V = exp(C_+) G_V exp(C_-)$, where $G_V$ is the stabilizer of V in G. To obtain this result we compare several subsemigroups of G specified by the grading and the positive cone $C_U$ of U. In particular, we show that the orbit U(G)V, endowed with the inclusion order, is an ordered symmetric space covering the adjoint orbit $Ad(G)h$, endowed with the partial order defined by~$C_U$.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42892192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums 循环商奇点和Dedekind和的多维连分数
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-12-01 DOI: 10.1215/21562261-2019-0032
T. Ashikaga
{"title":"Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums","authors":"T. Ashikaga","doi":"10.1215/21562261-2019-0032","DOIUrl":"https://doi.org/10.1215/21562261-2019-0032","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45412965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Local theta lift for p-adic unitary dual pairs U(2)×U(1) and U(2)×U(3) p进酉对偶U(2)×U(1)和U(2)×U(3)的局部升力
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-12-01 DOI: 10.1215/21562261-2019-0033
Yasuhiko Ikematsu
{"title":"Local theta lift for p-adic unitary dual pairs U(2)×U(1) and U(2)×U(3)","authors":"Yasuhiko Ikematsu","doi":"10.1215/21562261-2019-0033","DOIUrl":"https://doi.org/10.1215/21562261-2019-0033","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48865873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras 与极大抛物子代数相关的标量广义Verma模的可约性
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-12-01 DOI: 10.1215/21562261-2019-0027
Haian He, Toshihisa Kubo, R. Zierau
{"title":"On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras","authors":"Haian He, Toshihisa Kubo, R. Zierau","doi":"10.1215/21562261-2019-0027","DOIUrl":"https://doi.org/10.1215/21562261-2019-0027","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47302573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 10
A critical point analysis of Landau–Ginzburg potentials with bulk in Gelfand–Cetlin systems Gelfand-Cetlin体系中带体朗道-金兹堡势的临界点分析
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-11-11 DOI: 10.1215/21562261-2021-0002
Yunhyung Cho, Yoosik Kim, Y. Oh
{"title":"A critical point analysis of Landau–Ginzburg potentials with bulk in Gelfand–Cetlin systems","authors":"Yunhyung Cho, Yoosik Kim, Y. Oh","doi":"10.1215/21562261-2021-0002","DOIUrl":"https://doi.org/10.1215/21562261-2021-0002","url":null,"abstract":"Using the bulk-deformation of Floer cohomology by Schubert cycles and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function, we prove that every complete flag manifold $mathrm{Fl}(n)$ ($n geq 3$) with a monotone Kirillov--Kostant--Souriau symplectic form carries a continuum of non-displaceable Lagrangian tori which degenerates to a non-torus fiber in the Hausdorff limit. In particular, the Lagrangian $S^3$-fiber in $mathrm{Fl}(3)$ is non-displaceable, answering the question of which was raised by Nohara--Ueda who computed its Floer cohomology to be vanishing.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43157906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
The saturation number of c-bounded stable monomial ideals and their powers c有界稳定单项式理想的饱和数及其幂
IF 0.6 4区 数学
Kyoto Journal of Mathematics Pub Date : 2019-09-24 DOI: 10.1215/21562261-2022-0013
Reza Abdolmaleki, J. Herzog, G. Zhu
{"title":"The saturation number of c-bounded stable monomial ideals and their powers","authors":"Reza Abdolmaleki, J. Herzog, G. Zhu","doi":"10.1215/21562261-2022-0013","DOIUrl":"https://doi.org/10.1215/21562261-2022-0013","url":null,"abstract":"Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of $cb$-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated $cb$-bounded strongly stable ideals. We also provide explicit formulas for the saturation number $sat(I)$ of Veronese type ideals $I$. Using this formula, we show that $sat(I^k)$ is quasi-linear from the beginning and we determine the quasi-linear function explicitly.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45726332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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