-
作者：Valko, Benedek; Virag, Balint
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
摘要：We provide a precise coupling of the finite circular beta ensembles and their limit process via their operator representations. We prove explicit bounds on the distance of the operators and the corresponding point processes. We also prove an estimate on the beta-dependence of the Sine(beta) process.
-
作者：Bobkov, S. G.; Chistyakov, G. P.; Goetze, F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.
-
作者：Gerstenberg, Julian
作者单位：Leibniz University Hannover
摘要：A hypergraph (V, E) is called an interval hypergraph if there exists a linear order l on V such that every edge e is an element of E is an interval w.r.t. l; we also assume that {j} is an element of E for every j is an element of V. Our main result is a de Finetti-type representation of random exchangeable interval hypergraphs on N (EIHs): the law of every EIH can be obtained by sampling from some random compact subset K of the triangle {(x, y) : 0 <= x <= y <= 1} at i.i.d. uniform positions U...
-
作者：Sabot, Christophe; Zeng, Xiaolin
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Consider a negatively drifted one-dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time has the law of a three-dimensional Bessel bridge. In this paper, we give a generalization of this result to a family of Brownian motions with interacting drifts, indexed by the vertices of a conductance network. The hitting times are equal in law to the inv...
-
作者：Ding, Jian; Wirth, Mateo
作者单位：University of Pennsylvania
摘要：We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather precise estimates of percolation pro...
-
作者：Spinka, Yinon
作者单位：University of British Columbia
摘要：It has been shown by van den Berg and Steif (Ann. Probab. 27 (1999) 1501-1522) that the subcritical and critical Ising model on Z(d) is a finitary factor of an i.i.d. process (ffiid), whereas the super-critical model is not. In fact, they showed that the latter is a general phenomenon in that a phase transition presents an obstruction for being ffiid. The question remained whether this is the only such obstruction. We make progress on this, showing that certain spatial mixing conditions (notio...
-
作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If (G(n))(n >= 1) is a sequence of transitive graphs converging locally to a transitive graph G and lim sup(n ->infinity) pc(G(n)) < 1, then p(c)(G(n)) -> p(c)(G) as n -> infinity. We verify this conjecture under the additional hypothesis that there is a uniform exponential lower bound on the volume growth of the graphs in question. The result is new even i...
-
作者：Janvresse, Elise; Roy, Emmanuel; de la Rue, Thierry
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Picardie Jules Verne (UPJV); Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie
摘要：In this paper, we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation are all ergodic, the only ergodic splitting is the obvious one, that is, a collection of independent Poisson processes. We apply this result to the case of a marked Poisson process: under the same hypothesis, the marks are necessarily independent of the point process and i.i.d. Under additional assumptions on the t...
-
作者：Kopel, Phil; Orourke, Sean; Vu, Van
作者单位：University of Colorado System; University of Colorado Boulder; Yale University
摘要：We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of M independent i.i.d. random matrices, as M is fixed, and the sizes of the matrices tend to infinity. This generalizes an earlier result of Tao and the third author for the case M = 1. We also prove Gaussian limits for the centered linear spectral statistics of products of M independent i.i.d. random matrices. This is done in two steps. First, we establish the result...
-
作者：Le Jan, Yves; Raimond, Olivier
作者单位：Universite Paris Saclay
