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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
摘要：We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particul...
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作者：Johnston, Tom; Kronenberg, Gal; Roberts, Alexander; Scott, Alex
作者单位：University of Bristol; University of Oxford
摘要：In the graph shotgun assembly problem, we are given the balls of radius r around each vertex of a graph and asked to reconstruct the graph. We study the shotgun assembly of the Erd & odblac;s-R & eacute;nyi random graph G(n,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {G}}(n,p)$$\end{document} for a ...
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作者：Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we continue the study of large N problems for the Wick renormalized linear sigma model, i.e. N-component Phi 4 model, in two spatial dimensions, using stochastic quantization methods and Dyson-Schwinger equations. We identify the large N limiting lawof a collection ofWick renormalized O(N) invariant observables. In particular, under a suitable scaling, the quadratic observables converge in the large N limit to amean-zero (singular) Gaussian field denoted byQwith an explicit covar...
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作者：Osman, Mohammed
作者单位：University of London; Queen Mary University London
摘要：We prove that the local eigenvalue statistics in the bulk for complex random matrices with independent entries whose r-th absolute moment decays as N-1-(r-2)& varepsilon; for some & varepsilon;>0 are universal. This includes sparse matrices whose entries are the product of a Bernouilli random variable with mean N-1+& varepsilon; and an independent complex-valued random variable. By a standard truncation argument, we can also conclude universality for complex random matrices with 4+& varepsilon...
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作者：Angel, Omer; Senizergues, Delphin
作者单位：University of British Columbia; Centre National de la Recherche Scientifique (CNRS)
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作者：Dolgopyat, Dmitry; Hafouta, Yeor
作者单位：University System of Maryland; University of Maryland College Park; State University System of Florida; University of Florida
摘要：We prove Berry-Esseen theorems for sums Sn=& sum;j=0n-1fj degrees Tj-1 degrees & ctdot;degrees T1 degrees T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S_n=\sum _{j=0}<^>{n-1}f_j\circ T_{j-1}\circ \cdots \circ T_1\circ T_0$$\end{document} where fj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
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作者：Chen, Xinxin; Lin, Shen
作者单位：Beijing Normal University; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We study the critical branching random walk on Zd started from a distant point x and conditioned to hit some compact set K in Zd . We are interested in the occupation time in K and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order & Vert;x & Vert;4-d in dimensions d <= 3 , of order log & Vert;x & Vert; in dimension d=4 , and of order 1 in dimensions d >= 5 . The corresponding weak convergences are also established. These res...
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作者：Higgs, Frankie
作者单位：University of Bath
摘要：We analyse the aggregate Loewner evolution (ALE), introduced in 2018 by Sola, Turner and Viklund to generalise versions of diffusion limited aggregation (DLA) in the plane using complex analysis. They showed convergence of the ALE for certain parameters to a single growing slit. Started from a non-trivial initial configuration of k needles and the same parameters, we show that the small-particle scaling limit of ALE is the Laplacian path model, introduced by Carleson and Makarov, in which the ...
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作者：Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia
作者单位：University of Strathclyde; Utah System of Higher Education; University of Utah; Pompeu Fabra University; Barcelona School of Economics
摘要：We consider a parabolic stochastic partial differential equation (SPDE) on [0, 1] that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusion coefficient and a drift coefficient that is locally Lipschitz and satisfies an LlogL growth condition. We prove that the SPDE is well posed when the initial data is in L-2[0,1]. This solves a strong form of an open problem.
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作者：Galicza, Pal; Pete, Gabor
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Budapest University of Technology & Economics
摘要：For a sequence of Boolean functions fn:{-1,1}Vn ->{-1,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n : \{-1,1\}<^>{V_n} \longrightarrow \{-1,1\}$$\end{document}, with random input given by some probability measure Pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
