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Electronic Communications in Probability最新文献

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Moments of the superdiffusive elephant random walk with general step distribution 具有一般步长分布的超扩散大象随机漫步矩
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-30 DOI: 10.1214/22-ecp485
J. Kiss, B'alint VetHo
{"title":"Moments of the superdiffusive elephant random walk with general step distribution","authors":"J. Kiss, B'alint VetHo","doi":"10.1214/22-ecp485","DOIUrl":"https://doi.org/10.1214/22-ecp485","url":null,"abstract":"We consider the elephant random walk with general step distribution. We cal-culate the first four moments of the limiting distribution of the position rescaled by n α in the superdiffusive regime where α is the memory parameter. This extends the results obtained by Bercu in [Ber17].","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46680065","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: 0
Dynamical noise sensitivity for the voter model 投票者模型的动态噪声敏感性
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-24 DOI: 10.1214/22-ECP483
Gideon Amir, Omer Angel, Rangel Baldasso, R. Peretz
{"title":"Dynamical noise sensitivity for the voter model","authors":"Gideon Amir, Omer Angel, Rangel Baldasso, R. Peretz","doi":"10.1214/22-ECP483","DOIUrl":"https://doi.org/10.1214/22-ECP483","url":null,"abstract":"We study how the consensus opinion of the voter model on finite graphs varies in light of noise sensitivity with respect to both the initial opinions and the dynamics. We first prove that the final opinion is stable with respect to small perturbations of the initial configuration. Different effects are observed when a perturbation is introduced in the dynamics governing the evolution of the process, and the final opinion is noise sensitive in this case. Our proofs rely on the relationship between the voter model and coalescing random walks, and on a precise description of this evolution when we have coupled dynamics.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47034968","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: 0
Explicit formulas concerning eigenvectors of weakly non-unitary matrices 关于弱非酉矩阵特征向量的显式公式
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-24 DOI: 10.1214/22-ECP507
Guillaume Dubach
{"title":"Explicit formulas concerning eigenvectors of weakly non-unitary matrices","authors":"Guillaume Dubach","doi":"10.1214/22-ECP507","DOIUrl":"https://doi.org/10.1214/22-ECP507","url":null,"abstract":". We investigate eigenvector statistics of the Truncated Unitary ensemble TUE( N, M ) in the weakly non-unitary case M = 1 , that is when only one row and column are removed. We provide an explicit description of generalized overlaps as deterministic functions of the eigenvalues, as well as a method to derive an exact formula for the expectation of diagonal overlaps (or squared eigenvalue condition numbers), conditionally on one eigenvalue. This complements recent results obtained in the opposite regime when M ≥ N , suggesting possible extensions to TUE( N, M ) for all values of M .","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49345961","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
An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion 高斯相关不等式在Kolmogorov扩散小偏差中的应用
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-14 DOI: 10.1214/22-ecp459
M. Carfagnini
{"title":"An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion","authors":"M. Carfagnini","doi":"10.1214/22-ecp459","DOIUrl":"https://doi.org/10.1214/22-ecp459","url":null,"abstract":"We consider an iterated Kolmogorov diffusion X t of step n . The small ball problem for X t is solved by means of the Gaussian correlation inequality. We also prove Chung’s laws of iterated logarithm for X t both at time zero and infinity.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48198342","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: 1
Marchenko-Pastur law for a random tensor model 随机张量模型的Marchenko-Pastur定律
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-08 DOI: 10.1214/23-ecp527
P. Yaskov
{"title":"Marchenko-Pastur law for a random tensor model","authors":"P. Yaskov","doi":"10.1214/23-ecp527","DOIUrl":"https://doi.org/10.1214/23-ecp527","url":null,"abstract":"We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with symmetric random tensors formed by $binom{n}{d}$ different products of $d$ variables chosen from $n$ independent standardized random variables. We find optimal sufficient conditions for this distribution to be the Marchenko-Pastur law in the case $d=d(n)$ and $ntoinfty$. Our conditions reduce to $d^2=o(n)$ when the variables have uniformly bounded fourth moments. The proofs are based on a new concentration inequality for quadratic forms in symmetric random tensors and a law of large numbers for elementary symmetric random polynomials.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44325550","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: 1
TAP equations are repulsive TAP方程具有排斥性
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-11-03 DOI: 10.1214/22-ecp505
Stephan Gufler, Jan Lukas Igelbrink, N. Kistler
{"title":"TAP equations are repulsive","authors":"Stephan Gufler, Jan Lukas Igelbrink, N. Kistler","doi":"10.1214/22-ecp505","DOIUrl":"https://doi.org/10.1214/22-ecp505","url":null,"abstract":"We show that for low enough temperatures, but still above the AT line, the Jacobian of the TAP equations for the SK model has a macroscopic fraction of eigenvalues outside the unit interval. This provides a simple explanation for the numerical instability of the fixed points, which thus occurs already in high temperature. The insight leads to some algorithmic considerations on the low temperature regime, also briefly discussed.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43099481","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
The Boué–Dupuis formula and the exponential hypercontractivity in the Gaussian space bou<s:1> - dupuis公式与高斯空间中的指数超收缩性
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-10-28 DOI: 10.1214/22-ECP461
Yuu Hariya, S. Watanabe
{"title":"The Boué–Dupuis formula and the exponential hypercontractivity in the Gaussian space","authors":"Yuu Hariya, S. Watanabe","doi":"10.1214/22-ECP461","DOIUrl":"https://doi.org/10.1214/22-ECP461","url":null,"abstract":"This paper concerns a variational representation formula for Wiener functionals. Let B = { B t } t ≥ 0 be a standard d -dimensional Brownian motion. Boué and Dupuis (1998) showed that, for any bounded measurable functional F ( B ) of B up to time 1 , the expectation E (cid:104) e F ( B ) (cid:105) admits a variational representation in terms of drifted Brownian motions. In this paper, with a slight modification of insightful reasoning by Lehec (2013) allowing also F ( B ) to be a functional of B over the whole time interval, we prove that the Boué–Dupuis formula holds true provided that both e F ( B ) and F ( B ) are integrable, relaxing conditions in earlier works. We also show that the formula implies the exponential hypercontractivity of the Ornstein–Uhlenbeck semigroup in R d , and hence, due to their equivalence, implies the logarithmic Sobolev inequality in the d -dimensional Gaussian space.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41409898","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
On random disc-polygons in a disc-polygon 在圆盘多边形中的随机圆盘多边形上
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-10-23 DOI: 10.1214/23-ecp515
F. Fodor, P. Kevei, V. V'igh
{"title":"On random disc-polygons in a disc-polygon","authors":"F. Fodor, P. Kevei, V. V'igh","doi":"10.1214/23-ecp515","DOIUrl":"https://doi.org/10.1214/23-ecp515","url":null,"abstract":"We prove asymptotic formulas for the expectation of the vertex number and missed area of uniform random disc-polygons in convex disc-polygons. Our statements are the $r$-convex analogues of the classical results of R'enyi and Sulanke (1964) about random polygons in convex polygons.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42366962","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: 1
Global existence for quadratic FBSDE systems and application to stochastic differential games 二次型FBSDE系统的全局存在性及其在随机微分对策中的应用
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-10-04 DOI: 10.1214/23-ecp513
Joe Jackson
{"title":"Global existence for quadratic FBSDE systems and application to stochastic differential games","authors":"Joe Jackson","doi":"10.1214/23-ecp513","DOIUrl":"https://doi.org/10.1214/23-ecp513","url":null,"abstract":"In this note, we extend some recent results on systems of backward stochastic differential equations (BSDEs) with quadratic growth to the case of coupled forward-backward stochastic differential equations (FBSDEs). We work in a Markovian setting, and use results from the quadratic BSDE literature together with PDE techniques to obtain a-priori estimates which lead to an existence result. We also identify a general class of stochastic differential games whose corresponding FBSDE systems are covered by our main existence result. This leads to the existence of Markovian Nash equilibria for such games.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48112569","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
Overdamped limit at stationarity for non-equilibrium Langevin diffusions 非平衡朗格万扩散的过阻尼平稳极限
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-10-04 DOI: 10.1214/22-ecp447
Pierre Monmarch'e, M. Ramil
{"title":"Overdamped limit at stationarity for non-equilibrium Langevin diffusions","authors":"Pierre Monmarch'e, M. Ramil","doi":"10.1214/22-ecp447","DOIUrl":"https://doi.org/10.1214/22-ecp447","url":null,"abstract":"In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equiva-lently in the Smoluchowski-Kramers vanishing mass limit), toward a tensor product of the stationary distribution of the corresponding overdamped process and of a Gaussian distribution.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45289593","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
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