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作者：Gwynne, Ewain; Holden, Nina; Miller, Jason
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLE kappa curve for kappa not equal 4. Our proof is based on the relationship between SLE and Liouville quantum gravity together with the one-dimensional KPZ formula of Rhodes and Vargas (ESAIM Probab Stat 15:358-371, 2011) and the KPZ formula of Gwynne et al. (Ann Probab, 2...
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作者：Caputo, Pietro; Quattropani, Matteo
作者单位：Roma Tre University
摘要：We consider sparse digraphs generated by the configuration model with given in-degree and out-degree sequences. We establish that with high probability the cover time is linear up to a poly-logarithmic correction. For a large class of degree sequences we determine the exponent gamma >= 1 of the logarithm and show that the cover time grows as n log(gamma) (n), where n is the number of vertices. The results are obtained by analysing the extremal values of the stationary distribution of the digra...
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作者：Borga, Jacopo
作者单位：University of Zurich
摘要：We set up a new notion of local convergence for permutations and we prove a characterization in terms of proportions of consecutive pattern occurrences. We also characterize random limiting objects for this new topology introducing a notion of shift-invariant property (corresponding to the notion of unimodularity for random graphs). We then study two models in the framework of random pattern-avoiding permutations. We compute the local limits of uniform rho-avoiding permutations, for vertical b...
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作者：Nourdin, Ivan; Nualart, David
作者单位：University of Luxembourg; University of Kansas
摘要：Let X = {X-n}(n is an element of Z) be zero-mean stationary Gaussian sequence of random variables with covariance function rho satisfying rho(0) = 1. Let phi : R -> R be a function such that E[phi(X-0)(2)] < infinity and assume that phi has Hermite rank d >= 1. The celebrated Breuer-Major theorem asserts that, if Sigma(r is an element of Z) vertical bar rho(r)vertical bar(d) < infinity then the finite dimensional distributions of 1/root n Sigma(left perpendicularn.right perpenducular-1)(i=0) p...
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作者：Gwynne, Ewain; Holden, Nina; Sun, Xin
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We introduce a general technique for proving estimates for certain random planar maps which belong to the gamma-Liouville quantum gravity (LQG) universality class for gamma is an element of(0,2) The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d. increments via a mating-of-trees bijection, and includes the uniform infinite planar triangulation (UIPT;gamma=8/3and planar maps weighted by the number of different spanning trees (...
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作者：Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer
作者单位：Stanford University; Carnegie Mellon University; Weizmann Institute of Science
摘要：We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in d >= 3 with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger (J Stat Phys 171:543-598, 2018).
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作者：Holmes, Mark; Perkins, Edwin
作者单位：University of Melbourne; University of British Columbia
摘要：We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin. Conditions are given on the random sets and an associated ancestral relation under which, conditional on longterm survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a...
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作者：Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction theta of a Fisher-von Mises-Langevin distribution on the p-dimensional unit hypersphere is equal to a given direction theta 0. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension pn goes to infinity at an arbitrary rate with the sample size n...
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作者：Backhoff-Veraguas, Julio; Bartl, Daniel; Beiglboeck, Mathias; Eder, Manu
作者单位：University of Vienna
摘要：A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion-Nadal and Talay i...
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作者：Addario-Berry, L.; Cairns, H.; Devroye, L.; Kerriou, C.; Mitchell, R.
作者单位：McGill University; Cornell University; McGill University
摘要：We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (Pemantle's Min-Plus Binary Tree, 2017.[math.PR]), and to the critical random hierarchical lattice studied by Hambly and Jordan (Adv Appl Probab 36(3):824-838, 2004. 10.1239/aap/1093962236). We prove distributional convergence for the processes, after rescaling,...
