arXiv:2609. 11837v1 Announce Type: cross Abstract: We study the nonlocal continuity equation \[ \partial_t\mu_b =\operatorname{div}\!
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arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
arXiv:2609. 12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz.
The paper introduces a new simultaneous pointwise majorization framework for Banach‑valued stochastic processes that possess finite‑metric mixed‑tail increments. By assuming an anchored process satisfies a tail bound involving multiple pseudo‑metrics and orders, the authors derive a high‑probability envelope that holds uniformly over the index set, with terms expressed through integrals of log‑covering numbers and distance functions. This result generalizes single‑metric sub‑Weibull bounds and, in the Gaussian case, improves existing pointwise upper bounds by removing extraneous logarithmic factors.
arXiv:2609.01576v1 Announce Type: cross Abstract: Classical chaining controls an indexed stochastic process through a single worst-case bound, which can obscure substantial variation across the index...
arXiv:2510. 22778v3 Announce Type: replace-cross Abstract: We develop a free-probabilistic framework for denoising diffusion, in which the data is a self-adjoint operator and its law a spectral distribution.
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.