-
作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Los Angeles; Queens University - Canada; Saarland University
摘要：We study sequences of noncommutative random variables which are invariant under quantum transformations coming from an orthogonal quantum group satisfying the easiness condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S-n, O-n, which is ba...
-
作者：Grimmett, Geoffrey R.; Holroyd, Alexander E.
作者单位：University of Cambridge; University of British Columbia; Microsoft
摘要：Does there exist a Lipschitz injection of Z(d) into the open set of a site percolation process on Z(D), if the percolation parameter p is sufficiently close to 1? We prove a negative answer when d = D and also when d >= 2 if the Lipschitz constant M is required to be I. Earlier work of Dirr, Dondl, Grimmett, Holroyd and Scheutzow yields a positive answer for d < D and M = 2. As a result, the above question is answered for all d, D and M. Our proof in the case d = D uses Tucker's lemma from top...
-
作者：Seppaelaeinen, Timo
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study a (1 + 1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with exponential or geometric weights is special among growth models, namely, both permit explicit calculations. With appropriate boundary conditions, the polymer with log-gamma weights satisfies an analogue of Burke's theorem for queues. Building on this, we prove ...
-
作者：Budhiraja, Amarjit; Dupuis, Paul; Fischer, Markus
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：We study large deviation properties of systems of weakly interacting particles modeled by Ito stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation ...
-
作者：Chaumont, Loic; Kyprianou, Andreas; Carlos Pardo, Juan; Rivero, Victor
作者单位：Universite d'Angers; University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：For a positive self-similar Markov process, X, we construct a local time for the random set, Theta, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its past supremum. Next, we define and study the ladder process (R, H) associated to a positive self-similar Markov process X, namely a bivariate Markov process with a scaling property whose coordinates are the right inverse of the local time of the random set The...
-
作者：Jin, Xiong
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.
-
作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m - (m(2/alpha) - Delta)(alpha/2)] in C-1,C-1 open sets. Here m > 0 and alpha is an element of (0, 2). The estimates are uniform in m is an element of (0, M] for each fixed M > 0. Letting m down arrow 0, we recover the Dirichlet heat kernel estimates for Delta(alpha/2) := -(-Delta)(alpha/2) in C-1,C-1 open sets obtained in [14]. Sharp ...
-
作者：Ben Arous, Gerard; Fribergh, Alexander; Gantert, Nina; Hammond, Alan
作者单位：New York University; University of Munster; University of Oxford
摘要：We consider a biased random walk X-n on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant gamma = gamma(beta) is an element of (0, 1), depending on the bias beta, such that vertical bar X-n vertical bar is of order n(gamma). Denoting Delta(n) the hitting time of level n, we prove that Delta(n)/n(1/gamma) is tight. Moreover, we show that Delta(n)/n(1/gamma) does not converge in law (at least for large values of beta). We prove that alo...
-
作者：Benjamini, Itai; Boucheron, Stephane; Lugosi, Gabor; Rossignol, Raphael
作者单位：Weizmann Institute of Science; Pompeu Fabra University; ICREA; Pompeu Fabra University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c is an element of ]0, 1[, the property that the random sub-graph contains a giant component of size c vertical bar V vertical bar has a sharp threshold.
-
作者：Bianchi, Alessandra; Bovier, Anton; Ioffe, Dmitry
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bonn; Technion Israel Institute of Technology
摘要：We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a meta-stable set. In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.
