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作者：Wang, Haoyu
作者单位：Yale University
摘要：We prove the first explicit rate of convergence to the Tracy-Widom distribution for the fluctuation of the largest eigenvalue of sample covariance matrices that are not integrable. Our primary focus is matrices of type X*X and the proof follows the Erdos-Schlein-Yau dynamical method. We use a recent approach to the analysis of the Dyson Brownian motion from (J. Eur. Math. Soc. (JEMS) 24 (2022) 2823-2873) to obtain a quantitative error estimate for the local relaxation flow at the edge. Togethe...
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作者：Gundlach, Rowel; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：We analyse the cluster discovered by invasion percolation on a branching process with a power-law offspring distribution. Invasion percolation is a paradigm model of self-organised criticality, where criticality is approach without tuning any parameter. By performing invasion percolation for n steps, and letting n -> infinity, we find an infinite subtree, called the invasion percolation cluster (IPC). A notable feature of the IPC is its geometry that consists of a unique path to infinity (also...
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作者：Biskup, Marek; Krieger, Andrew
作者单位：University of California System; University of California Los Angeles
摘要：We consider a long-range percolation graph on Z(d) where, in addition to the nearest-neighbor edges of Z(d) , distinct x,y is an element of Z(d) are connected by an edge independently with probability asymptotic to beta|x - y|(-s), for s is an element of (d, 2 d) , beta > 0 and |center dot| a norm on R-d. We first show that, for all but perhaps a countably many beta > 0, the graph-theoretical (a.k.a. chemical) distance between typical vertices at |center dot|-distance r is, with high probabili...
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作者：Bernstein, Daniel Irving; Dewar, Sean; Gortler, Steven J.; Nixon, Anthony; Sitharam, Meera; Theran, L. ouis
作者单位：Tulane University; University of Bristol; Harvard University; Lancaster University; State University System of Florida; University of Florida; University of St Andrews
摘要：The maximum likelihood threshold (MLT) of a graph G is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of the MLT in terms of rigidity-theoretic properties of G and use this characterization to give new combinatorial lower bounds on the MLT of any graph. We use the new lower bounds to give high-probability guarantees on the maximum likelihood thresholds of sparse ...
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作者：Chakrabarty, A. rijit; Samorodnitsky, Gennady
作者单位：Indian Statistical Institute; Cornell University
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作者：Roberts, Asher
作者单位：City University of New York (CUNY) System
摘要：In this paper we quantify the rate of convergence in Selberg's central limit theorem for log |zeta (1/2 + it)| based on the method of proof given by the same rate of convergence of (log log log T )2/root log log T as Selberg in (In 1989) Univ (1992) 367-385) in the Kolmogorov distance by using the Dudley distance instead. We also prove the theorem for the multivariate case given by same rate of convergence as in the single variable case.
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作者：Xu, Wei
作者单位：Beijing Institute of Technology
摘要：This paper is concerned with the evolution dynamics of local times ofa spectrally positive stable process in the spatial direction. The main resultsstate that conditioned on the finiteness of the first time at which the local timeat zero exceeds a given value, the local times at positive half line are equal indistribution to the unique solution of a stochastic Volterra equation driven bya Poisson random measure whose intensity coincides with the L & eacute;vy measure.This helps us to provide n...
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作者：Legried, Brandon; Roch, Sebastien
作者单位：University System of Georgia; Georgia Institute of Technology; University of Wisconsin System; University of Wisconsin Madison
摘要：Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many biological applications, it has played a key role in elucidating the statistical performance of phylogeny estimation methods. Here we establish a formal connection to another important bioinformatics problem, multiple sequence alignment, where one attempts ...
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作者：Ganassali, Luca; Lelarge, Marc; Massoulie, Laurent
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Inria
摘要：Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We study the likelihood ratio test and obtain sufficient conditions under which this task is impossible or feasible. We propose MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign to succeed in polynomial time at partial alignment whenever tree detection is feasi...
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作者：Cotsakis, Ryan; Di Bernardino, Elena; Duval, Celine
作者单位：Universite Cote d'Azur; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The excursion set of a C2 smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to observations at discrete points in space. It has been reported that for specific regular lattices of points in dimensions 2 and 3, the usual approximation of the surface area of the excursions does not converge when the lattice becomes dense in the domain of observatio...
