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作者：Borodin, Alexei; Corwin, Ivan; Sasamoto, Tomohiro
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Columbia University; Chiba University
摘要：We prove duality relations for two interacting particle systems: the q-deformed totally asymmetric simple exclusion process (q-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents, respectively. Duality implies that they solve systems of ODEs. These systems are integrable and for particular step and half-stationary initial data we use a nested contour integral ansatz t...
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作者：Tong, Xin Thomson; van Handel, Ramon
作者单位：New York University; Princeton University
摘要：The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional distributions given one of the components. Such questions play a fundamental role in the ergodic theory of nonlinear filters. In the setting of Harris chains, conditional ergodicity has been established under general nondegeneracy assumptions. Unfortunately, Markov...
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作者：Dirksen, Sjoerd
作者单位：University of Bonn
摘要：Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove Ito isomorphisms for L-p-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) L-p-space, which may be of independent interest. As a by-product of our proof, we observe so...
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作者：Bordenave, Charles; Caputo, Pietro
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Roma Tre University
摘要：We consider n x n Hermitian matrices with i.i.d. entries X-ij whose tail probabilities P(vertical bar X-ij vertical bar >= t) behave like e(-at alpha) for some a > 0 and alpha is an element of (0, 2). We establish a large deviation principle for the empirical spectral measure of X/root n with speed n(1+alpha/2) with a good rate function J(mu) that is finite only if mu is of the form mu = mu(sc) boxed plus nu for some probability measure nu on R, where boxed plus denotes the free convolution an...
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作者：Armstrong, Scott N.; Smart, Charles K.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Universite PSL; Universite Paris-Dauphine; Massachusetts Institute of Technology (MIT)
摘要：We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is only assumed to have a finite dth moment, where d is the dimension. In the general stationary-ergodic framework, we show that the equation homogenizes to a deterministic, uniformly elliptic equation, and we obtain an explicit estimate of the effective ellipti...
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作者：Jara, M.; Landim, C.; Teixeira, A.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：Consider a sequence of possibly random graphs G(N) = (V-N, E-N), N >= 1, whose vertices's have i.i.d. weights {W-x(N) : x is an element of V-N} with a distribution belonging to the basin of attraction of an alpha-stable law, 0 < alpha < 1. Let X-t(N), t >= 0, be a continuous time simple random walk on G(N) which waits a mean W-x(N) exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topolo...
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作者：Castell, Fabienne; Guillotin-Plantard, Nadine; Pene, Francoise; Schapira, Bruno
作者单位：Aix-Marseille Universite; 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; CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Random walks in random scenery are processes defined by Z(n) := Sigma(n)(k=1) xi(X1+ ...+Xk), where basically (X-k, k >= 1) and (xi(y), y is an element of Z) are two independent sequences of i.i.d. random variables. We assume here that X-1 is Z-valued, centered and with finite moments of all orders. We also assume that xi(0) is Z-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that (n(-3/4)Z([nt]), t >= 0) converges in distribution as n --> infinity toward ...
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作者：Goetze, Friedrich; Venker, Martin
作者单位：University of Bielefeld
摘要：We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or determinantal representation, the local correlations in the bulk coincide in the limit of infinitely many particles with those known from random Hermitian matrices; in particular they can be expressed as determinants of the so-called sine kernel. These results m...
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作者：Sly, Allan; Sun, Nike
作者单位：University of California System; University of California Berkeley; Australian National University; Stanford University
摘要：We establish that the normalized log-partition function of any two-spin system on bipartite locally tree-like graphs converges to a limiting free energy density which coincides with the (nonrigorous) Bethe prediction of statistical physics. Using this result, we characterize the local structure of two-spin systems on locally tree-like bipartite expander graphs without the use of the second moment method employed in previous works on these questions. As a consequence, we show that for both the ...
