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作者：Guerra, Enrique; Valle, Glauco; Vares, Maria Eulalia
作者单位：Hebrew University of Jerusalem; Universidade Federal do Rio de Janeiro
摘要：We study ballisticity conditions for d-dimensional random walks in strong mixing environments, with underlying dimension d >= 2. Specifically, we introduce an effective polynomial condition similar to that given by Berger et al. (Comm. Pure Appl. Math. 77:1947-1973, 2014). In a mixing setup we prove that this condition implies the corresponding stretched exponential decay, and obtain an annealed functional central limit theorem for the random walk process centered at the limiting velocity. Thi...
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作者：Lammers, Piet
作者单位：Universite Paris Saclay
摘要：The interest is in models of integer-valued height functions on shift-invariant planar graphs whose maximum degree is three. We prove delocalisation for models induced by convex nearest-neighbour potentials, under the condition that each potential function is an excited potential, that is, a convex symmetric potential function V with the property that V(+/- 1) <= V(0) + log 2. Examples of such models include the discrete Gaussian and solid-on-solid models at inverse temperature beta <= log 2, ...
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作者：Gonzalez, Isaac; Horton, Emma; Kyprianou, Andreas E.
作者单位：University of Bath; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：Suppose that X = (X-t, t >= 0) is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities P-delta x, when issued from a unit mass at x is an element of E. For a general setting in which the first moment semigroup of X displays a Perron-Frobenius type behaviour, we show that, for k >= 2 and any positive bounded measurable function f on E, lim(t ->infinity) gk(t)E-delta x[< f, X-t >(k)] = C-k(x, f), where the constant C-k(x, ...
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作者：Aoun, Richard; Sert, Cagri
作者单位：New York University; New York University Abu Dhabi; University of Zurich
摘要：The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space M, we obtain explicit bounds that depend only on M, the size of support of the measure as in the classical case of sums of independent random variables, and on the norm of the driving probability measure in the left regular representation of the group of isometries...
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作者：Leonard, Christian
摘要：Motivated by entropic optimal transport, we are interested in the Feynman-Kac formula associated to the parabolic equation (L + V)g = 0 with a final nonnegative boundary condition and a Markov generator L := partial derivative(t) + b.del + Delta(a)/2. It is well-known that when the drift b, the diffusion matrix a and the scalar potential V are regular enough and not growing too fast, the classical solution g of this PDE, is represented by the Feynman-Kac formula g(t)(x) = E-R[exp (integral([t,...
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作者：Erny, Xavier; Locherbach, Eva; Loukianova, Dasha
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the convergence of N-particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position and on the empirical measure of the system. Jumps are simultaneous, that is, at each jump time, all particles of the system are affected by this jump and receive a random jump height that is centred and scaled in N-1/2. This particular scaling i...
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作者：Zhang, Xicheng; Zhu, Rongchan; Zhu, Xiangchan
作者单位：Wuhan University; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which are not well-defined in the classical sense and are understood by using the paracontrolled distribution method introduced in (Gubinelli et al. in Forum Math Pi 3(6):1, 2015). By a new characterization of weighted Holder spaces and Zvonkin's transformation we prove some new a priori estimates, and therefore establish the global well-posedness for singular HJB equations. As applicatio...
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作者：Liu, Zhipeng
作者单位：University of Kansas
摘要：We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times, and its limit as the parameters go to infinity under the KPZ scaling.
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作者：Bufetov, Alexey; Nejjar, Peter
作者单位：Leipzig University; University of Bonn; University of Bonn
摘要：This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N. Our main result is that for particle densities in (0, 1), the total-variation cutoff window of ASEP is N-1/3 and the cutoff profile is 1 - F-GUE, where F-GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbe and Lacoin. Our proof combines coupling arguments, the result of Tracy-Widom about fluctuations of ASEP starte...
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作者：Deuschel, Jean-Dominique; Guo, Xiaoqin
作者单位：Technical University of Berlin; University of Wisconsin System; University of Wisconsin Madison; University System of Ohio; University of Cincinnati
摘要：We prove a quenched local central limit theorem for continuous-time random walks in Z(d), d >= 2, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green's function.
