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作者：Kabluchko, Zakhar; Marynych, Alexander
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：Let xi 1, xi 2, ... be a sequence of independent copies of a random vector in R-d having an absolutely continuous distribution. Consider a random walk S-i := xi(1) + ... + ... + xi(i), and let C-n,C-d := conv(0, S-1, S-2, ..., S-n) be the convex hull of the first n+ 1 points it has visited. The polytope C-n,C-d is called k-neighborly if for any indices 0 <= i(1) < ... < i(k) <= n the convex hull of the k points S-i1 , ..., S-ik is a (k - 1)-dimensional face of C-n,C-d. We study the probability...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
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作者：Lee, Jungkyoung; Seo, Insuk
作者单位：Seoul National University (SNU); Seoul National University (SNU)
摘要：In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between neighborhoods of local minima, compared to the reversible process considered in Bovier et al. (J Eur Math Soc 6:399-424, 2004). Therefore, by adding non-reversibility to the model, we can indeed accelerate the metastable transition. Our proof is based on the po...
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作者：Athreya, Jayadev S.; Mj, Mahan; Roy, Parthanil
作者单位：University of Washington; University of Washington Seattle; Tata Institute of Fundamental Research (TIFR); Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We study extreme values of group-indexed stable random fields for discrete groups G acting geometrically on spaces X in the following cases: (1) G acts properly discontinuously by isometries on a CAT(-1) space X, (2) G is a lattice in a higher rank Lie group, acting on a symmetric space X, and (3) G is the mapping class group of a surface acting on its Teichmuller space. The connection between extreme values and the geometric action is mediated by the action of the group G on its limit set equ...
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作者：Bobrowski, Omer
作者单位：Technion Israel Institute of Technology; University of London; Queen Mary University London
摘要：We study the homology of random Cech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity'-the stage where the random complex is dense enough, so that its homology stabilizes and becomes isomorphic to that of the underlying topological space. Our results form a comprehensive high-dimensional analogue of well-known phenomena related to connectivity in the Erdos-Renyi graph and random geometric graphs. We first prove that there is a sequence of sharp phase ...
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作者：Marcus, Adam W.; Spielman, Daniel A.; Srivastava, Nikhil
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Yale University; University of California System; University of California Berkeley
摘要：We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh and Szego in different contexts, and have been studied for a century. The asymmetric additive convolution, and the connection of all of them with random matrices, is new. By develo...
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作者：Au, Benson
作者单位：University of California System; University of California Berkeley
摘要：Let (sigma((i))(N))(i is an element of I) be a family of symmetric permutations of the entries of a Wigner matrix W-N. We characterize the limiting traffic distribution of the corresponding family a o) of dependent Wigner matrices (W-N(N)sigma(i))(i is an element of I) in terms of the geometry of the permutations. We also consider the analogous problem for the limiting joint distribution of (W-N(N)sigma(i))(i is an element of I). In particular, we obtain a description in terms of semicircular ...
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作者：Parraud, Felix
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Kyoto University
摘要：Let U-N = (U-1(N), ..., U-p(N)) be a p-tuple of N x N independent Haar unitary matrices and Z(NM) be any family of deterministic matrices in M-N(C) circle times M-M(C). Let P be a self-adjoint non-commutative polynomial. In Voiculescu (Int Math Res Notices 1:41-63, 1998), Voiculescu showed that the empirical measure of the eigenvalues of this polynomial evaluated in Haar unitary matrices and deterministic matrices converges towards a deterministic measure defined thanks to free probability the...
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作者：Klein, Thierry; Lagnoux, Agnes; Petit, Pierre
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite de Toulouse; Universite de Toulouse - Jean Jaures; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the model of hashing with linear probing and we establish the moderate and large deviations for the total displacement in sparse tables. In this context, Weibull-like-tailed random variables appear. Deviations for sums of such heavy-tailed random variables are studied in Nagaev (Theory Probab Appl 14(1):51-64, 1969; Theory Probab Appl 14(2):193-208, 1969). Here we adapt the proofs therein to deal with conditioned sums of such variables and solve the open question in Gamboa et al. (...
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作者：Faggionato, Alessandra
作者单位：Sapienza University Rome
摘要：We consider continuous-time random walks on a random locally finite subset of R d with random symmetric jump probability rates. The jump range can be unbounded. We assume some second-moment conditions and that the above randomness is left invariant by the action of the group G = R-d or G = Z(d). We then add a site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits...
