Related papers: From minimal embeddings to minimal diffusions
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
We study the regularity of a diffusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our…
We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical…
This paper studies small-time behavior at the supremum of a diffusion process. For a solution to the SDE $\mathrm{d} X_t=\mu(X_t)\mathrm{d} t+\sigma(X_t)\mathrm{d} W_t$ (where $W$ is a standard Brownian motion) we consider…
We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy…
The symmetric simple exclusion process (SEP) is a paradigmatic model of diffusion in a single-file geometry, in which the particles cannot cross. In this model, the study of currents have attracted a lot of attention. In particular, the…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi\'c and Urusov (2012c)…