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作者：Zhu, Qingsan
作者单位：Nanjing University of Aeronautics & Astronautics
摘要：We study critical branching random walks and introduce the branching capacity and related concepts for any finite subset of Zd,d >= 5 . By introducing these concepts, we can obtain analogues of various classical results for random walks. In this paper, we develop the basic properties of the branching capacity and show that it is closely related to the probability of visiting a fixed finite set by a critical branching random walk starting from a distant point, as well as to the conditional dist...
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作者：Ryou, Donggeun; Suomala, Ville
作者单位：Indiana University System; Indiana University Bloomington; University of Oulu
摘要：We consider multifractal Mandelbrot cascades supported on planar C2 curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure.
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作者：Bansaye, Vincent; Berah, Tresnia; Cloez, Bertrand
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Institut Agro; Universite de Montpellier; INRAE
摘要：We consider branching processes for structured populations: each individual is characterised by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may survive and grow and the trait distribution converges to a probability measure. The branching process is then expected to be driven by the positive triplet of first eigenvalue problem of the first moment semigroup. Under the assumption of convergence of the renorm...
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作者：Grama, Ion; Quint, Jean-Francois; Xiao, Hui
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper represents the first step toward achieving this goal, specifically entailing the construction of a novel entity - the target harmonic measure. This measure, together with the harmonic function, serves as a pivotal component in establishing the conditioned local limit theorem. Using a reversal identity, we in...
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作者：Deuschel, Jean-Dominique; Kumagai, Takashi; Slowik, Martin
作者单位：Technical University of Berlin; Waseda University; University of Mannheim
摘要：In this paper we consider a time-continuous random walk in Z(d) in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover, that they are bounded from below but unbounded from above with finite first moment. We derive sharp on-diagonal estimates for the annealed first and second discrete space derivative of the heat kernel which then yield local limit theorems for the corresponding kernels...
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作者：Denisov, Denis; Fitzgerald, Will; Wachtel, Vitali
作者单位：University of Manchester; University of Bielefeld
摘要：The Airy line ensemble is a random collection of continuous ordered paths that plays an important role within random matrix theory and the Kardar-Parisi-Zhang universality class. The aim of this paper is to prove a universality property of the Airy line ensemble. We study growing numbers of i.i.d. continuous-time random walks which are then conditioned to stay in the same order for all time using a Doob h-transform. We consider a general class of increment distributions; a sufficient condition...
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作者：Chiarini, Alberto; Pasqui, Emanuele
摘要：We study the discrete Gaussian free field (harmonic crystal) on Z(d) , d >= 3 , with uniformly elliptic and bounded random conductances sampled according to a sufficiently mixing environment measure. We consider the hard wall event that the field is non-negative on the discrete blow-up of a bounded regular domain V subset of R-d , and establish a quenched large deviation asymptotic for its probability. The asymptotic rate is characterized by the essential supremum of the on-site variances and ...
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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：Feldheim, Naomi; Haimi, Antti; Koliander, Gunther; Romero, Jose Luis
作者单位：Bar Ilan University; Austrian Academy of Sciences; University of Vienna
摘要：We study zero sets of twisted stationary Gaussian random functions on the complex plane, i.e., Gaussian random functions that are stochastically invariant under the action of the Weyl-Heisenberg group. This model includes translation-invariant Gaussian entire functions (GEFs), and also many other non-analytic examples, in which case winding numbers around zeros can be either positive or negative. We investigate zero statistics both when zeros are weighted with their winding numbers (charged ze...
