Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation the gradient potential function. In several real-world scenarios, obtaining evaluations might either be computationally expensive, or simply impossible. this work, we propose analyze stochastic zeroth-order algorithms discretizing overdamped unde...

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method pos...

We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2 and discuss the nature of their ground states, collective excitations, and relation to the more fam...

Abstract Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have achieved. Here, we study thermalization small that interact with large chaotic environments under the consideration Schrödinger evolution composite systems, from perspective zeroth law thermodynamics. Namely, consider a system is brought into contact environmental sys...

We prove that that the time averaged consistency error of the Nth approximate deconvolution LES model converges to zero uniformly in the kinematic viscosity and in the Reynolds number as the cube root of the averaging radius. We also give a higher order but non-uniform consistency error bound for the zeroth order model directly from the Navier-Stokes equations.