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作者：Calka, Pierre; Demichel, Yann
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively random sets as the union of adjacent tiles from these rescaled tessellations. We encode this geometric construction into a combinatorial object, namely a multitype Galton-Watson tree. Our main result concerns the geometric properties of the limiting planar set. In particular, we show that both box and Hausdorff dimens...
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作者：He, Yukun
作者单位：Fudan University
摘要：Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} be the adjacency matrix of the Erd & odblac;s-R & eacute;nyi directed graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
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作者：Kohler-Schindler, Laurin; Lehmkuehler, Matthis
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a critical Fortuin-Kasteleyn (FK) percolation with cluster weight q is an element of[1,4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \in [1,4)$$\end{document} in the plane, and color its clusters in red (respectively blue) with probability r is an element of(0,1)\documentclass[12pt]{minimal} \usep...
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作者：Bao, Zhigang; Lee, Jaehun; Xu, Xiaocong
作者单位：Hong Kong University of Science & Technology
摘要：In this paper, we study the smallest non-zero eigenvalue of the sample covariance matrices S(Y) = YY *, where Y = ( yi j) is an M x N matrix with iid mean 0 variance N -1 entries. We consider the regime M = M(N) and M/ N. c8. R\{1} as N. 8. It is known that for the extreme eigenvalues of Wigner matrices and the largest eigenvalue of S(Y), a weak 4thmoment condition is necessary and sufficient for the Tracy-Widom law (Ding and Yang in Ann Appl Probab 28(3):1679-1738, 2018. https:// doi.org/10.1...
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作者：Melbourne, James; Nayar, Piotr; Roberto, Cyril
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Warsaw; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable, answering a 2010 question of Bobkov and Madiman [1]. This gives a sharp reversal of the celebrated entropy maximization theorem due to Boltzmann, in the log-concave case. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequaliti...
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作者：Menshikov, Mikhail; Popov, Serguei; Wade, Andrew
作者单位：Durham University; Universidade do Porto
摘要：We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. Under appropriate hypotheses on the jump rates (uniformly bounded rates is sufficient) and started from an initial condition that is a finite perturbation of the close-packed ...
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作者：Qin, Shuo
摘要：Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions d=1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1,2$$\end{document}, and that it is transient for all reinforcement parameters in ...
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作者：Abdalla, Pedro; Mendelson, Shahar
作者单位：University of California System; University of California Irvine; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We construct an estimator for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements X1,& mldr;,XN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1,\ldots ,X_N$$\end{document} of X and the wanted confidence level. We show under minimal assumptions on...
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作者：Groathouse, Sean; Rassoul-Agha, Firas; Seppalainen, Timo; Sorensen, Evan
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：We give an explicit description of a family of jointly invariant measures of the KPZ equation singled out by asymptotic slope conditions. These are couplings of Brownian motions with drift, and can be extended to a cadlag process indexed by all real drift parameters. We name this process the KPZ horizon (KPZH). As a corollary, we resolve a recent conjecture by showing the existence of a random, countably infinite dense set of drift values at which the Busemann process of the KPZ equation is di...
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作者：He, Jimmy
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type B an...
