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作者：Norris, James; Silvestri, Vittoria; Turner, Amanda
作者单位：University of Cambridge; Sapienza University Rome; University of Leeds
摘要：We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that a...
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作者：Carlier, Guillaume; Friesecke, Gero; Voegler, Daniela
作者单位：Universite PSL; Universite Paris-Dauphine; Technical University of Munich
摘要：We present a novel analogue for finite exchangeable sequences of the de Finetti, Hewitt and Savage theorem and investigate its implications for multi-marginal optimal transport (MMOT) and Bayesian statistics. If (Z(1), ..., Z(N)) is a finitely exchangeable sequence of N random variables taking values in some Polish space X, we show that the law mu(k) of the first k components has a representation of the form mu(k )= integral F-P1/N(X) (N,k)(lambda) d alpha(lambda) for some probability measure ...
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作者：Aldous, David; Contat, Alice; Curien, Nicolas; Henard, Olivier
作者单位：University of California System; University of California Berkeley; Universite Paris Saclay
摘要：Let (A(u) : u is an element of B) be i.i.d. non-negative integers that we interpret as car arrivals on the vertices of the full binary tree B. Each car tries to park on its arrival node, but if it is already occupied, it drives towards the root and parks on the first available spot. It is known (Bahl et al. in Parking on supercritical Galton-Watson trees, arXiv:1912.13062, 2019; Goldschmidt and Przykucki in Comb Probab Comput 28:23-45, 2019) that the parking process on B exhibits a phase trans...
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作者：Augeri, Fanny; Butez, Raphael; Zeitouni, Ofer
作者单位：Weizmann Institute of Science; Universite Paris Cite; Universite de Lille; New York University
摘要：We prove a central limit theorem for the real part of the logarithm of the characteristic polynomial of random Jacobi matrices. Our results cover the G beta E models for beta > 0.
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作者：Dario, Paul; Harel, Matan; Peled, Ron
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Northeastern University; Tel Aviv University
摘要：We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, in the following cases. It is shown that for real-valued random-field random surfaces of the & nabla; phi type with a uniformly convex interaction potential: (i) The gradient of the surface delocalizes in dimensions 1 <= d <= 2 and localizes...
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作者：Bryc, Wlodek; Kuznetsov, Alexey; Wang, Yizao; Wesolowski, Jacek
作者单位：University System of Ohio; University of Cincinnati; York University - Canada; Warsaw University of Technology
摘要：We provide a probabilistic description of the stationary measures for the open KPZ on the spatial interval [0, 1] in terms of a Markov process Y, which is a Doob's h transform of the Brownian motion killed at an exponential rate. Our work builds on a recent formula of Corwin and Knizel which expresses the multipoint Laplace transform of the stationary solution of the open KPZ in terms of another Markov process T: the continuous dual Hahn process with Laplace variables taking on the role of tim...
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作者：Dolgopyat, Dmitry; Hafouta, Yeor
作者单位：University System of Maryland; University of Maryland College Park; University System of Ohio; Ohio State University
摘要：We prove a Berry-Esseen theorem and Edgeworth expansions for partial sums of the form S-N = Sigma(N)(n=1) f(n)(X-n, Xn+1), where {X-n} is a uniformly elliptic inhomogeneous Markov chain and {f(n)} is a sequence of uniformly bounded functions. The Berry-Esseen theorem holds without additional assumptions, while expansions of order 1 hold when {f(n)} is irreducible, which is an optimal condition. For higher order expansions, we then focus on two situations. The first is when the essential suprem...
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作者：Inoue, Akihiko
作者单位：Hiroshima University
摘要：We derive novel explicit formulas for the inverses of truncated block Toeplitz matrices that correspond to a multivariate minimal stationary process. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the spectral density of the process. The derivation of the formulas is based on a recently developed finite prediction theory applied to the dual process of the stationary process. We illustrate the usefulness of the formulas by two applications. T...
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作者：Dewan, Vivek; Muirhead, Stephen
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Melbourne
摘要：We prove upper bounds on the one-arm exponent eta(1) for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percolation of Gaussian fields, the arguments apply to other models in the Bernoulli percolation universality class, including Poisson-Voronoi and Poisson-Boolean percolation. More precisely, in dimension d = 2 we prove that eta(1) <= 1/3 for continuous Gaussian fields with rapid correlation decay (e.g. the Bargmann-Fock f...
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作者：Lacoin, Hubert; Rhodes, Remi; Vargas, Vincent
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Aix-Marseille Universite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field X defined on a subset of R-d by the exponential of its cosine, namely exp (alpha integral cos(beta X)). It has gathered significant attention due to its importance in quantum field theory and to its connection with the study of log-gases in statistical mechanics. In spite of its relatively simple definition, the model has a very rich phenomenology. While the integral integral cos(beta X) can be defined prop...
