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作者：Schmid, Dominik
作者单位：University of Bonn
摘要：We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a segment of size N with open boundaries. We focus on the maximal current phase and prove that the mixing time is of order N3/2, up to logarithmic corrections. In the triple point, where the TASEP with open boundaries approaches the Uniform distribution on the state space, we show that the mixing time is precisely of order N3/2. This is conjectured to be the correct order of the mixing time for a wide range of...
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作者：Hutchroft, Tom; Michta, Emmanue; Slade, Gordon
作者单位：California Institute of Technology; University of British Columbia
摘要：We consider percolation on Z(d) and on the d-dimensional discrete torus, in dimensions d >= 11 for the nearest-neighbour model and in dimensions d > 6 for spread-out models. For Z(d) we employ a wide range of techniques and previous results to prove that there exist positive constants c and C such that the slightly subcritical two-point function and one-arm probabilities satisfy Ppc-epsilon(0 <-> x) <= C/||x||(d-2) e(-c epsilon 1/2) ||x|| c/r(2)e -C epsilon(1/2r) <= Ppc-epsilon (0 <-> partial ...
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作者：Duminil-Copin, Hugo; Rivera, Alejandro; Rodriguez, Pierre-Francois; Vanneuville, Hugo
作者单位：University of Geneva; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：For the Bargmann-Fock field on R-d with d >= 3, we prove that the critical level l(c) (d) of the percolation model formed by the excursion sets {f >= l} is strictly positive. This implies that for every l sufficiently close to 0 (in particular for the nodal hypersurfaces corresponding to the case l = 0), {f = l} contains an unbounded connected component that visits most of the ambient space. Our findings actually hold for a more general class of positively correlated smooth Gaussian fields wit...
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作者：Addario-Berry, Louigi; Barrett, Jordan
作者单位：McGill University
摘要：We consider invasion percolation on the complete graph K-n, started from some number k(n) of distinct source vertices. The outcome of the process is a forest consisting of k(n) trees, each containing exactly one source. Let M-n be the size of the largest tree in this forest. Logan, Molloy and Pralat (2018) proved that if k(n)/n(1/3)-> 0 then M-n/n -> 1 in probability. In this paper, we prove a complementary result: if k(n)/n(1/3)-> infinity, then M-n/n -> 0 in probability. This establishes the...
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作者：Fox, Jacob; Kwan, Matthew; Spink, Hunter
作者单位：Stanford University
摘要：The classical Erdos-Littlewood-Offord theorem says that for nonzero vectors a1, ... , an E Rd, any x E Rd, and uniformly random (xi 1,. . . ,xi n) E {-1, 1}n, we have Pr(a1 xi 1 + middot middot middot + an xi n = x) = O(n-1/2). In this paper, we show that Pr(a1 xi 1 + middot middot middot + an xi n E S) < n-1/2+o(1) whenever S is definable with respect to an o-minimal structure (e.g., this holds when S is any algebraic hypersurface), under the necessary condition that it does not contain a lin...
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作者：Dey, Partha s.; Terlov, G. R. I. G. O. R. Y.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In the seventies, Charles Stein revolutionized the way of proving the cen-tral limit theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to adapt and strengthen this method to a variety of different set-tings and other limiting distributions. However, it has not been yet extended to study conditional convergences. In this article we develop a novel approach, using Stein's method for exchangeable ...
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作者：Cordero-Erausquin, Dario; Rotem, Liran
作者单位：Sorbonne Universite; Universite Paris Cite; Technion Israel Institute of Technology
摘要：We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extend-ing previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance, to Cauchy measures as well. For the proof, new sharp weighted Poincare inequalities are obtained for even probability measures that are log-concave with respect to a rotation-ally invariant measure.
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作者：Dereudre, David; Vasseur, Thibaut
作者单位：Universite de Lille; Universite Paris Cite
摘要：For an inverse temperature /3 > 0, we define the /3-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = IlxII-s. We focus on the nonintegrable case d -1 < s < d. Our main result ensures, for any dimension d > 1 and inverse temperature /3 > 0, the existence of a /3-circular Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel s...
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作者：Xiao, Hui; Grama, Ion; Liu, Quansheng
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider (gn)n>1 a sequence of independent and identically distributed random matrices and the left random walk Gn := gn . . . g1, n > 1 on the general linear group GL(d, R). Under suitable conditions we establish a Bahadur-Rao-Petrov type large deviation expansion for the coefficient (f, Gnv) of the product Gn, where v & epsilon; Rd and f & epsilon; (Rd)*. In particular, we obtain an explicit rate function in the large deviation principle, thus im-proving significantly the known large deviati...
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作者：Conchon-Kerjan, Guillaume; Goldschmidt, Christina
作者单位：University of Bath; University of Oxford
摘要：We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail be-haviour with exponent alpha + 1, where alpha & ISIN; (1, 2). The limiting components are constructed from random R-trees encoded by the excursions above its run-ning infimum of a process whose law is locally absolutely continuous with respect to that of a spectrally positive alpha-stable Levy process. These spanning R-trees are measure-changed alpha-st...
