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作者：Lehmkuehler, Matthis; Qian, Wei; Werner, Wendelin
作者单位：University of Basel; University of Hong Kong; University of Cambridge
摘要：The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting Brownian loops in a planar domain that possesses some combinatorial features related to the notion of indistinguishability of bosons. The properly renormalized occupation time field of this collection of loops is known to be distributed like the properly defined square of a Gaussian free field. In the present paper, we study how much information these fields provide about the loop-soup. Among other thi...
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作者：Radhakrishnan, Ritvik Ramanan; Tassion, Vincent
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We discuss a general method to obtain quantitative improvements of correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}<^>2$$\end{document}. Our first result is that the two-arm exponent is strictly larger than twice...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile
摘要：We study cluster sizes in supercritical d-dimensional inhomogeneous percolation models with long-range edges -such as long-range percolation- and/or heavy-tailed degree distributions -such as geometric inhomogeneous random graphs and the age-dependent random connection model. Our focus is on large deviations of the size of the largest cluster in the graph restricted to a finite box as its volume tends to infinity. Compared to nearest neighbor Bernoulli bond percolation on Zd\documentclass[12pt...
