Related papers: The expected Euler characteristic approximation to…

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to…

We study power approximation formulas for peak detection using Gaussian random field theory. The approximation, based on the expected number of local maxima above the threshold $u$, $\mathbb{E}[M_u]$, is proved to work well under three…

We investigate the asymptotic variance of Gaussian nodal excursions in the Euclidean space, focusing on the case where the spectral measure has incommensurable atoms. This study requires to establish fine recurrence properties in 0 for the…

We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…

We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth…

Given any $\gamma>0$ and for $\eta=\{\eta_v\}_{v\in \mathbb Z^2}$ denoting a sample of the two-dimensional discrete Gaussian free field on $\mathbb Z^2$ pinned at the origin, we consider the random walk on~$\mathbb Z^2$ among random…

We analyze the distance $\mathcal{R}_T(u)$ between the first and the last passage time of $\{X(t)-ct:t\in [0,T]\}$ at level $u$ in time horizon $T\in(0,\infty]$, where $X$ is a centered Gaussian process with stationary increments and…

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using…

We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter $H<1/2$. Our methods are based on an equidistant discretization of the…

This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one…

Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…

For a smooth, stationary Gaussian field $f$ on Euclidean space with fast correlation decay, there is a critical level $\ell_c$ such that the excursion set $\{f\geq\ell\}$ contains a (unique) unbounded component if and only if $\ell<\ell_c$.…

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…

We describe an exact algorithm for finding the best 2-OPT move which, experimentally, was observed to be much faster than the standard quadratic approach. To analyze its average-case complexity, we introduce a family of heuristic procedures…

We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…

We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…

Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants $u,T$, define the set of conjunctions $C_{[0,T],u}:=\{t\in…

The purpose of this note is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler…

We consider a $d$-dimensional random field $u=(u(x), x\in D)$ that solves a system of elliptic stochastic equations on a bounded domain $D\subset \mathbb{R}^k$, with additive white noise and spatial dimension $k=1,2,3$. Properties of $u$…

We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively…