Related papers: Stein's method for steady-state diffusion approxim…

In this paper, we quantify some known approximation to the Curie-Weiss model via applying the Stein method to the Markov chain whose stationary distribution coincides with Curie-Weiss model.

Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible target distributions. We do so by using the generator approach…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…

We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

We challenge a fundamental assumption of diffusion models, namely, that a large number of latent-states or time-steps is required for training so that the reverse generative process is close to a Gaussian. We first show that with careful…

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly…

The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…

We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs…

Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…

Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…