相关论文: On the limiting behaviour of some nonlocal seminor…

We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)-spaces,…

In order to determine the origin of discontinuities which arise when the semiclassical propagator is employed to describe an infinitely long and infinitesimally thin solenoid carrying magnetic flux, we give a systematic derivation of the…

We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.

We develop a general distributional theory of fractional (an)isotropic Sobolev spaces associated with the non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$.

We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated…

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…

We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling…

The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.

Recent experiments (G. Ariel, et al., Nature Comm. 6, 8396 (2015)) revealed an intriguing behavior of swarming bacteria: they fundamentally change their collective motion from simple diffusion into a superdiffusive L\'{e}vy walk dynamics.…

We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…

We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient…

A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…

In this work, we consider a class of second order uniformly elliptic operators with smooth and bounded coefficients. We provide some estimates on the norm of the semigroup generated by these operators acting on weighted Sobolev spaces,…

The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary…

Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic…

We show that interactions in quantum spin liquids can result in non-Hermitian phenomenology that differs qualitatively from mean-field expectations. We demonstrate this in two prominent cases through the effects of phonons and disorder on a…

It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can be measured in terms of suitable Gagliardo seminorms. We…

We consider the ordinary or fractional Laplacian plus a homogeneous, scaling-critical drift term. This operator is non-symmetric but homogeneous, and generates scales of $L^p$-Sobolev spaces which we compare with the ordinary homogeneous…

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…

We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth;…