Related papers: The high-dimensional asymptotics of first order me…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
Information flow or information transfer is an important concept in dynamical systems which has applications in a wide variety of scientific disciplines. In this study, we show that a rigorous formalism can be established in the context of…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
Let $k,d $ be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a $d$-dimensional Poisson Boolean model with balls of fixed radius is of order $k$, as the…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
Flow-based generation in high-dimensional spaces is difficult because velocity prediction requires modeling high-dimensional noise, even when data has strong low-rank structure. We present Asymmetric Flow Modeling (AsymFlow), a…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…