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作者：Gwynne, Ewain; Sung, Jinwoo
作者单位：University of Chicago
摘要：A Liouville quantum gravity (LQG) surface is a natural random twodimensional surface, initially formulated as a random measure space and later as a random metric space. We show that the LQG measure can be recovered as the Minkowski measure with respect to the LQG metric, answering a question of Gwynne and Miller (Invent. Math. 223 (2021) 213-333). As a consequence, we prove that the metric structure of a gamma -LQG surface determines its conformal structure for every gamma is an element of (0,...
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作者：Maini, Leonardo; Nourdin, Ivan
作者单位：University of Luxembourg
摘要：Let B = (Bx)(x is an element of Rd) be a collection of N(0, 1) random variables forming a real -valued continuous stationary Gaussian field on R-d, and set C(x -y) = E[BxBy]. Let yo : R -> R be such that E[phi(N)(2)] < infinity with N similar to N(0, 1), let R be the Hermite rank of yo, and consider Y-t = integral(tD) phi(B-x)dx, t > 0 with D subset of R-d compact. Since the pioneering works from the 1980s by Breuer, Dobrushin, Major, Rosenblatt, Taqqu and others, central and noncentral limit ...
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作者：Hao, Zimo; Zhang, Xicheng; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we study singular kinetic equations on R-2d by the paracontrolled distribution method introduced in Gubinelli, Imkeller and Perkowski (Forum Math. Pi 3 (2015) e6-75). We first develop paracontrolled calculus in the kinetic setting and use it to establish the global well-posedness for the linear singular kinetic equations under the assumptions that the products of singular terms are well defined. We also demonstrate how the required products can be defined in the case that singula...
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作者：Harris, Simon; Johnston, Samuel g. G.; Pardo, Juan carlos
作者单位：University of Auckland; University of London; King's College London
摘要：Consider a population evolving as a critical continuous-time Galton- Watson (GW) tree. Conditional on the population surviving until a large time T, sample k individuals uniformly at random (without replacement) from amongst those alive at time T. What is the genealogy of this sample of individuals? In cases where the offspring distribution has finite variance, the probabilistic properties of the joint ancestry of these k particles are well J. Probab. 24 (2019) 1-35). In the present article, w...
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作者：Biskup, Marek; Louidor, Oren
作者单位：University of California System; University of California Los Angeles; Technion Israel Institute of Technology
摘要：We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root, we prove that, in the limit as the depth of the tree tends to infinity, the suitably scaled and centered maximal time spent at any leaf converges to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale like object associated with square-root local-ti...
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作者：Dominguez, Tomas; Mourrat, Jean-christophe
作者单位：University of Toronto; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse regime, where the total number of nodes diverges while the average degree of a given node remains bounded. Our main contributions are a conjecture for the limit of this quantity, which we express in terms of a Hamilton-Jacobi equation posed over a space of probabi...
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作者：Zhang, Lingfu
作者单位：University of California System; University of California Davis
摘要：We consider the Metropolis biased card shuffling (also called the multispecies ASEP on a finite interval or the random Metropolis scan). Its convergence to stationarity was believed to exhibit a total -variation cutoff, and that was proved a few years ago by Labbe and Lacoin (Ann. Probab. 47 (2019) 1541-1586). In this paper, we prove that (for N cards) the cutoff window is in the order of N1/3, and the cutoff profile is given by the Tracy-Widom GOE distribution function. This confirms a conjec...
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作者：Lipnowski, Michael; Wright, Lex
作者单位：University System of Ohio; Ohio State University; University of Michigan System; University of Michigan
摘要：We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than 3/16-epsilon goes to zero as the genus goes to infinity.
