arXiv:2609. 11837v1 Announce Type: cross Abstract: We study the nonlocal continuity equation \[ \partial_t\mu_b =\operatorname{div}\!
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.
arXiv:2608.25279v1 Announce Type: cross Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
arXiv:2609. 04578v1 Announce Type: cross Abstract: We study stochastic gradient descent with random reshuffling for finite sums \[ F(x)=\frac1n\sum_{i=1}^n f_i(x).
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv:2608. 23462v1 Announce Type: cross Abstract: We establish a strong averaging principle for fast-slow stochastic differential equations with a time-dependent scale-separation parameter $(\varepsilon_t)_{t \geq 0}$ satisfying $\varepsilon_t \to 0$ as $t \to \infty$.