Related papers: Annealing diffusions in a slowly growing potential

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker…

For any $N\ge 2$ and $\aa:=(\aa_1,\cdots, \aa_{N+1})\in (0,\infty)^{N+1}$, let $\mu^{(N)}_{\aa}$ be the corresponding Dirichlet distribution on $\DD:= \big\{ x=(x_i)_{1\le i\le N}\in [0,1]^N:\ \sum_{1\le i\le N} x_i\le 1\big\}.$ We prove…

Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with…

We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…

In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a…

In this note, we will survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity…

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than…

In this paper, we present different proofs of very recent results on the necessary as well as sufficient conditions on the decrease of the potential at infinity for the validity of effective range formulas in 3-D in low energy potential…

We consider several local versions of the doubling condition and Poincar\'e inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding…

We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian $H:\mathbb {R}^n\to \mathbb {R}$ in the regime of low temperature $\varepsilon$. We proof the Eyring-Kramers formula for the optimal constant in the…

We prove existence of minimizers for the sharp Poincar\'e-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are not necessarily bounded, thus the relevant embeddings may…

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…

We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes of the corresponding diffusions. In…

Given a noisy linear measurement $y = Ax + \xi$ of a distribution $p(x)$, and a good approximation to the prior $p(x)$, when can we sample from the posterior $p(x \mid y)$? Posterior sampling provides an accurate and fair framework for…

We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…

Let $\mathcal S^2$ be the Stepanov space and let $ \lambda_n\uparrow\infty$. Let $(a_n)_{n\ge 1}$ be satisfying Wiener's condition $A:= \sum_{n\ge 1} \big(\sum_{k\, :\, n\le \lambda_k \le n+1}|a_k|\big)^2 <\infty$. We prove that $\big\|…

This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of…

We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly…

We study the long-time behavior of a particle in $\mathbb{R}^d$, $d \geq 2$, subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the divergence of a stationary random stream matrix $\mathbf{k}…