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Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this…
We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross-sectional shapes, including regular polygons and smoothed corner…
Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…
We study the problem of sampling from a distribution $\mu$ with density $\propto e^{-V}$ for some potential function $V:\mathbb R^d\to \mathbb R$ with query access to $V$ and $\nabla V$. We start with the following standard assumptions: (1)…
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration…
We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal across the entire High density phase and Low density phase. We…
We review recent advances in the numerical analysis of the Monge-Amp\`ere equation. Various computational techniques are discussed including wide-stencil finite difference schemes, two-scaled methods, finite element methods, and methods…
In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…
We introduce two probabilistic models of random log-concave polynomials, the uniform model and the beta model, and study the asymptotic distribution of their zeros in the complex plane. In the uniform model, we show that the empirical root…
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erd\"os-R\'enyi random graph. By analyzing finite graphs of increasing volume, as well as the graphon…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
We propose a novel kinetic Langevin sampler based on a specific splitting scheme using the exact harmonic Langevin integrator. For strongly log-concave target measures, the sampler exploits a decomposition of the strongly convex potential…
We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for…
We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…
We obtain sharp estimate on $p$-spectral gaps, or equivalently optimal constant in $p$-Poincar\'e inequalities, for metric measure spaces satisfying measure contraction property. We also prove the rigidity for the sharp $p$-spectral gap.
We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…