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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.
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作者：Miclo, Laurent
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
摘要：Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the exit time and position are almost independent. Since this is valid for any exiting extension of the state space, it corresponds to an instance of the metastability phenomenon. Simple examples at small...
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作者：Osada, Hirofumi
作者单位：Kyushu University
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作者：Gwynne, Ewain; Pfeffer, Joshua; Sheffield, Scott
作者单位：University of Chicago; Columbia University; Massachusetts Institute of Technology (MIT)
摘要：Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter gamma is an element of(0,2). We establish a strong confluence property for LQG geodesics, which generalizes a result proven by Angel, Kolesnik and Miermont for the Brownian map. Using this property, we also establish zero-one laws for the Hausdorff dimensions of geodesics, metric ball boundaries, and metric nets w.r.t. the Euclidean or L...
