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作者：Samson, Paul-Marie
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. Leonard by replacing W-2-Wasserstein geodesics by Schrodinger bridges in the definition of entropic curvature (Leonard in Discrete Contin Dyn Syst A 34(4):1533-1574, 2014; Ann Probab 44(3):1864-1915, 2016; in: Gigli N (ed) Measure theory in non-smooth spaces. Sciendo Migration,Warsaw, pp 194-242, 2017). As a remarkable fact, as a temperature parameter goes to zero, these Schrodinger bridg...
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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：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：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：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...
