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作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：In this paper, we consider the linearly reinforced and the once-reinforced random walk models in the transient phase on trees. We show the large deviations for the upper tails for both models. We also show the exponential decay for the lower tail in the once-reinforced random walk model. However, the lower tail is in polynomial decay for the linearly reinforced random walk model.
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作者：Rassoul-Agha, Firas; Seppaelaeinen, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and steps of the walk. The potential is subject to a moment assumption whose strictness is tied to the mixing of the environment, the best case being the i.i.d. environment. We prove that the infinite volume quenched point-to-point free energy exists and has a variational formula in terms of entropy. We establish regularity properties of the point-to...
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作者：Nolen, James
作者单位：Duke University
摘要：We consider solutions of an elliptic partial differential equation in with a stationary, random conductivity coefficient that is also periodic with period . Boundary conditions on a square domain of width are arranged so that the solution has a macroscopic unit gradient. We then consider the average flux that results from this imposed boundary condition. It is known that in the limit , this quantity converges to a deterministic constant, almost surely. Our main result is that the law of this r...
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作者：Romito, Marco
作者单位：University of Pisa
摘要：We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove pathwise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data.
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作者：Paouris, Grigoris; Pivovarov, Peter; Zinn, Joel
作者单位：Texas A&M University System; Texas A&M University College Station; University of Missouri System; University of Missouri Columbia
摘要：We prove a central limit theorem for the volume of projections of the cube onto a random subspace of dimension , when is fixed and . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.
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作者：Castillo, Ismael; Kerkyacharian, Gerard; Picard, Dominique
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.
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作者：Drewitz, Alexander; Sousi, Perla; Sun, Rongfeng
作者单位：Columbia University; University of Cambridge; National University of Singapore
摘要：We prove a new rearrangement inequality for multiple integrals, which partly generalizes a result of Friedberg and Luttinger (Arch Ration Mech 61:35-44, 1976) and can be interpreted as involving symmetric rearrangements of domains around . As applications, we prove two comparison results for general L,vy processes and their symmetric rearrangements. The first application concerns the survival probability of a point particle in a Poisson field of moving traps following independent L,vy motions....
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作者：Abramson, Joshua; Evans, Steven N.
作者单位：University of California System; University of California Berkeley
摘要：For , the -Lipschitz minorant of a function is the greatest function such that and for all , should such a function exist. If is a real-valued L,vy process that is not pure linear drift with slope , then the sample paths of have an -Lipschitz minorant almost surely if and only if . Denoting the minorant by , we investigate properties of the random closed set , which, since it is regenerative and stationary, has the distribution of the closed range of some subordinator made stationary in a suit...
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作者：Debussche, Arnaud; Romito, Marco
作者单位：University of Pisa
摘要：We prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic Navier-Stokes equations in dimension . In particular, under very mild assumptions on the noise, we prove that finite dimensional projections of the solutions have densities with respect to the Lebesgue measure which have some smoothness when measured in a Besov space. This is proved thanks to a new argument inspired by an idea introduced in (Fournier and Printe...
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作者：Basu, Riddhipratim; Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. Grimmett et al. (Random Str Algorithm 37(1):85-99, 2010) asked whether there exists an increasing -Lipschitz embedding from one i.i.d. Bernoulli sequence into an independent copy with positive probability. We give a positive answer for large enough . A closely related problem is to show that two independent Poisson processes on are roughly isometric (...
