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作者：Abdalla, Pedro; Mendelson, Shahar
作者单位：University of California Irvine; University of California System; University of California Irvine; ETH Zurich; 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：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...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva; Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon
摘要：This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions d > 6. We obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions d > 4 [Duminil-Copin and Panis, arXiv:2410.03649, (2024)].
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作者：Hazra, Rajat Subhra; den Hollander, Frank; Parvaneh, Azadeh
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：Let Gn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_n$$\end{document} be an undirected finite graph on n is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
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作者：Faggionato, Alessandra
作者单位：Sapienza University Rome
摘要：Mott's variable range hopping (v.r.h.) is the phonon-induced hopping of electrons in disordered solids (such as doped semiconductors) within the regime of strong Anderson localization. It was introduced by N. Mott to explain the anomalous low temperature conductivity decay in dimension d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...
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作者：Feng, Yuyang
作者单位：University of Chicago
摘要：We consider infinite random planar maps decorated by the critical Fortuin-Kasteleyn model with parameter q > 4. The paper demonstrates that when appropriately rescaled, these maps converge in law to the infinite continuum random tree as pointed metric-measure spaces, that is, with respect to the local Gromov-Hausdorff-Prokhorov topology. Furthermore, we also show that these maps do not admit any Fortuin-Kasteleyn loops with a macroscopic graph distance diameter. Our proof is based on Scott She...
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作者：Janson, Svante
作者单位：Uppsala University
摘要：Uncover the vertices of a given graph, deterministic or random, in uniformly random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization to a Gaussian process. This problem was studied by Hackl, Panholzer, and Wagner for the case when the graph is a uniformly random labelled tree; we generalize their result to more general graphs, including both other classes of random and non-rand...
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作者：Forsstrom, Malin P.; Gantert, Nina; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of {0,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{0,1\}$$\end{document}-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus ...
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作者：[Anonymous]
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作者：Archer, Eleanor; Hartarsky, Ivailo; Kolesnik, Brett; Olesker-Taylor, Sam; Schapira, Bruno; Valesin, Daniel
作者单位：Technische Universitat Wien; University of Warwick; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In Catalan percolation, all nearest-neighbour edges {i, i + 1} along Z are initially occupied, and all other edges are open independently with probability p. Open edges {i, j} are occupied if some pair of edges {i, k} and {k, j}, with i < k < j, become occupied. This model was introduced by Gravner and the third author, in the context of polluted graph bootstrap percolation. We prove that the critical pc is strictly between that of oriented site percolation on Z(2) and the Catalan growth rate ...
