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The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
We consider a random walk $S_k$ with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum $\sum_{k=1}^N f(S_k)$ with H\"older continuous test functions $f$, including the…
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
Affinity has proven to be a useful tool for quantifying the non-equilibrium character of time continuous Markov processes since it serves as a measure for the breaking of time reversal symmetry. It has recently been conjectured that the…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
Non-linear dynamics in the quantum random walk setting have been shown to enable conditional speedup of Grover's algorithm. We examine the mean field approximation required for the use of the Gross-Pitaevskii equation on identical bosons…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the…
We consider the problem of sketching the $p$-th frequency moment of a vector, $p>2$, with multiplicative error at most $1\pm \epsilon$ and \emph{with high confidence} $1-\delta$. Despite the long sequence of work on this problem, tight…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…