-
作者：Sasai, Takeyuki; Miyabe, Kenshi; Takemura, Akimichi
作者单位：University of Tokyo; Meiji University; Shiga University
摘要：We prove an Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales. Our proof is given in the framework of the game-theoretic probability of Shafer and Vovk. Like many other game-theoretic proofs, our proof is self-contained and explicit.
-
作者：Ding, Jian; Dunlap, Alexander
作者单位：University of Pennsylvania; Stanford University
摘要：Let {Y-B(x) : is an element of B} be a discrete Gaussian free field in a two-dimensional box of B side length S with Dirichlet boundary conditions. We study Liouville first-passage percolation: the shortest-path metric in which each vertex x is given a weight of e(gamma YB(x)) for some gamma > 0. We show that for sufficiently small but fixed gamma > 0, for any sequence of scales {S-k} there exists a subsequence along which the appropriately scaled and interpolated Liouville FPP metric converge...
-
作者：Domelevo, Komla; Petermichl, Stefanie
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We prove optimal L-2 bounds for a pair of Hilbert space valued differentially subordinate martingales under a change of law. The change of law is given by a process called a weight and sharpness, and in this context refers to the optimal growth with respect to the characteristic of the weight. The pair of martingales is adapted, uniformly integrable and cadlag. Differential subordination is in the sense of Burkholder, defined through the use of the square bracket. In the scalar dyadic setting ...
-
作者：Giunti, Arianna; Gu, Yu; Mourrat, Jean-Christophe
作者单位：University of Bonn; Carnegie Mellon University; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Came-Varopoulos type.
-
作者：Birkner, Matthias; Sun, Rongfeng
作者单位：Johannes Gutenberg University of Mainz; National University of Singapore
摘要：The lonely branching random walks on Z(d) is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. We show that if the symmetrized walk is recurrent, lonely branching random walks die out locally. Further-more, the same result holds if additional branching is allowed when the walk is not alone.
-
作者：Gerencser, Mate
作者单位：Institute of Science & Technology - Austria
摘要：The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly-and in a sense, arbitrarily-bad: as shown by Krylov [SIAM J. Math. Anal. 34 (2003) 1167-1182], for any alpha > 0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not alpha-Holder continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C-1 ...
-
作者：Aggarwal, Amol; Borodin, Alexei
作者单位：Harvard University; Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：In this paper, we consider two models in the Kardar-Parisi-Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call shape generalized step Bernoulli initial data) for both of these models that generalizes the step Bernoulli initial data studied in a number of recent works on the ASEP. Under this class of initial data, we analyze the current fluctuations of both the ASEP and stocha...
-
作者：Blaszczyszyn, B.; Yogeshwaran, D.; Yukich, J. E.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Lehigh University
摘要：Let P be a simple, stationary point process on R d having fast decay of correlations, that is, its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let P-n := P boolean AND W-n be its restriction to windows W-n := [- 1/2n(1/2), 1/2n(1/d)](d) subset of R-d. We consider the statistic := E-n(xi) := Sigma(x is an element of Pn) xi (x, P-n) where xi(x, P-n) denotes a score function representing the interaction of x with respect to P-...
-
作者：Thalmaier, Anton; Thompson, James
作者单位：University of Luxembourg
摘要：For a semigroup P-t generated by an elliptic operator on a smooth mani-fold M, we use straightforward martingale arguments to derive probabilistic formulae for P-t (V(f)), not involving derivatives of f, where V is a vector field on M. For nonsymmetric generators, such formulae correspond to the derivative of the heat kernel in the forward variable. As an application, these formulae can be used to derive various shift-Hamack inequalities.
-
作者：Chen, Le; Huang, Jingyu
作者单位：Nevada System of Higher Education (NSHE); University of Nevada Las Vegas; Utah System of Higher Education; University of Utah
摘要：We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on R-d (partial derivative/partial derivative t - 1/2 Delta)u(t, x) = rho(u(t , x)) (M) over dot (t , x), for measure-valued initial data, where (M) over dot is a spatially homogeneous Gaussian noise that is white in time and rho is Lipschitz continuous. These results are obtained under the condition that integral(Rd) (1 + vertical bar xi vertical bar(2))(alpha-1)...
