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作者：Abraham, Romain; Delmas, Jean-Francois; Nassif, Michel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We give an invariance principle for very general additive functionals of conditioned Bienayme-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Levy tree. This includes the case when the offspring distribution has finite variance (the Levy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending...
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作者：Bao, Zhigang; Wang, Dong
作者单位：Hong Kong University of Science & Technology; National University of Singapore
摘要：In this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source. We will focus on the critical regime of the Baik-Ben Arous-Peche (BBP) phase transition and establish the distribution of the eigenvectors associated with the leading eigenvalues. The distribution is given in terms of a determinantal point process with extended Airy kernel. Our result can be regarded as an eigenvector counterpart of the BBP eigenvalue phase transitio...
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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：Abe, Yoshihiro; Biskup, Marek
作者单位：Chiba University; University of California System; University of California Los Angeles
摘要：We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by N) versions D-N subset of Z(2) of bounded open domains D subset of R-2. Upon exit from D-N, the walk lands on a boundary vertex and then reenters D-N through a random boundary edge in the next step. In the parametrization by the local time at the boundary vertex we prove that, at times corresponding to a theta-multiple of the cover time of D-N, the sets of suitably defined lambda-thick (i.e.,...
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作者：Bakhtin, Yuri; Chen, Hong-Bin
作者单位：New York University
摘要：We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1 + 1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the...
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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...
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作者：De Masi, Anna; Marchesani, Stefano; Olla, Stefano; Xu, Lu
作者单位：University of L'Aquila; Gran Sasso Science Institute (GSSI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France
摘要：We study the one-dimensional asymmetric simple exclusion process on the lattice (1, ..., N) with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale N-a with a > 0. We prove that at the time scale N1+a the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates....
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作者：Dubail, Bastien; Massoulie, Laurent
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Given integers d >= 2, n >= 1, we consider affine random walks on torii (Z/nZ)(d) defined as Xt+1 = AX(t) + B-t mod n, where A is an element of GL(d)(Z) is a invertible matrix with integer entries and (B-t)(t >= 0) is a sequence of iid random increments on Z(d). We show that when A has no eigenvalues of modulus 1, this random walk mixes in O (log n log log n) steps as n -> infinity, and mixes actually in O (log n) steps only for almost all n. These results are similar to those of Chung et al. ...
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作者：Louf, Baptiste
作者单位：Uppsala University
摘要：We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.
