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作者：Menz, Georg; Schlichting, Andre
作者单位：Stanford University; University of Bonn
摘要：We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian H : R-n -> R in the regime of low temperature epsilon. We proof the Eyring-Kramers formula for the optimal constant in the Poincare (PI) and logarithmic Sobolev inequality (LSI) for the associated generator L = epsilon Delta - del H . del of the diffusion. The proof is based on a refinement of the two-scale approach introduced by Grunewald et al. [Ann. Inst. Henri Poincare Probab. Stat. 45 (2009) 302-351] a...
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作者：Mueller, Carl; Mytnik, Leonid; Perkins, Edwin
作者单位：University of Rochester; Technion Israel Institute of Technology; University of British Columbia
摘要：Motivated by Girsanov's nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) partial derivative u/partial derivative t = Delta/2 u(t, x) + vertical bar u(t, x)vertical bar(gamma) W(t, x), u(0, x) = 0 Here W is a space time white noise on R x R. More precisely, we show the above stochastic PDE has a nonzero solution for 0 < y < 3/4. Since u(t, x) = 0 solves the equation, it follows that solutions are neither unique in law nor ...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：We consider the initial boundary value problem ut = mu u(x) + 1/2u(xx) (t > 0, x >= 0) u(0, x) = f(x) (x >= 0), u(t)(t, 0) = vu(x) (t, 0) (t > 0) of Stroock and Williams [Comm. Pure Appl. Math. 58 (2005) 1116-1148] where, mu, v is an element of R and the boundary condition is not of Feller's type when v <0. We show that when f belongs to C-b(1) with f (infinity) = 0 then the following probabilistic representation of the solution is valid: u(t, x) = Ex[f'(Xt)integral(0) (lt0(x)) (e-2(v - mu)s) ...
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作者：Knowles, Antti; Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix H. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The isotropic semicircle law and deformation of Wigner matrices. Preprint] by admitting overlapping outliers and by computing the joint distribution of all outliers. In particular, we give a complete description of the failure of universality first observed in [Ann....
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this work, by using the Malliavin calculus, under Hormander's condition, we prove the existence of distributional densities for the solutions of stochastic differential equations driven by degenerate subordinated Brownian motions. Moreover, in a special degenerate case, we also obtain the smoothness of the density. In particular, we obtain the existence of smooth heat kernels for the following fractional kinetic Fokker Planck (nonlocal) operator: L-b((alpha)) := Delta(alpha/2)(v) + v . del(...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a sigma-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Levy-Ito representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.
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作者：Da Prato, Giuseppe; Lunardi, Alessandra
作者单位：Scuola Normale Superiore di Pisa; University of Parma
摘要：We consider an elliptic Kolmogorov equation lambda u - Ku = f in a separable Hilbert space H. The Kolmogorov operator K is associated to an infinite dimensional convex gradient system: dX = (AX - DU (X)) dt + dW (t), where A is a self-adjoint operator in H, and U is a convex lower semicontinuous function. Under mild assumptions we prove that for lambda > 0 and f is an element of L-2(H, v) the weak solution u belongs to the Sobolev space W-2,W-2 (H, v), where v is the log-concave probability me...
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作者：Duplantier, Bertrand; Rhodes, Remi; Sheffield, Scott; Vargas, Vincent
作者单位：Universite Paris Saclay; CEA; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Chemistry (INC); Massachusetts Institute of Technology (MIT)
摘要：In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove that for any constant K >= 1, the value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over K by value functions whose second-order derivatives are bounded by a constant times K. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.
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作者：Schuhmacher, Dominic; Stucki, Kaspar
作者单位：University of Bern; University of Gottingen
摘要：We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's meth...
