Related papers: A threshold phenomenon for random independent sets…
We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$…
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $P(\omega_j=0)=P(\omega_j=1)=1/2$ and all the choices are independent. For $0<a<1/2$, the measure $\mu_a$ is supported on $C_a$, the central…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
We consider $n$ independent random points uniformly distributed in the $d_n$-dimensional unit cube and study Pareto points, that is, points that do not coordinatewise dominate any other point. We identify the critical growth rate of $d_n$…
We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have…
We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $\phi_\lambda$ and define the value $r_\lambda = (\phi_\lambda|\phi_\lambda)/<\phi_\lambda|\phi_\lambda>$ that characterizes the phase rigidity…
We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…
We consider $Z^d$, with d bigger or equal to three. We investigate the vacant set of random interlacements in the strongly percolative regime, the vacant set of the simple random walk, and the excursion set above a given level of the…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of…
We study the stationary distribution of the (spread-out) $d$-dimensional contact process from the point of view of site percolation. In this process, vertices of $\mathbb{Z}^d$ can be healthy (state 0) or infected (state 1). With rate one…
In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold. We also determine thresholds…
We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\times d}$ is an i.i.d random matrix, $W\in\mathbb{R}^{d\times…
Developing an idea of M. Gromov, we study the intersection formula for random subsets with density. The \textit{density} of a subset $A$ in a finite set $E$ is defined by $dens A := \log_{|E|}(|A|)$. The aim of this article is to give a…
We prove that the Poisson-Boolean percolation on $\mathbb{R}^d$ undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a $5d-3$ finite moment (in particular we do not assume that the…
Near-threshold collectivization of continuum shell model eigenstates is investigated in $^{20}$O on the example of B(E$\lambda$) decays of 4$^+$ states in the vicinity of elastic and inelastic neutron threshold. Changes of the…
We study small time bounds for transition densities of convolution semigroups corresponding to pure jump L\'evy processes in $\mathbb{R}^{d}$, $d \geq 1$, including those with jumping kernels exponentially and subexponentially localized at…
In this paper, we find a full Lebesgue measure set of frequencies $\check \II\subset [0,1]\setminus \Q$ such that for any $(\alpha,\lambda)\in \check \II\times [24,\infty)$, the Hausdorff and box dimensions of the spectrum of the Sturmian…
The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can…
A strong law of large numbers for $d$-dimensional random projections of the $n$-dimensional cube is derived. It shows that with respect to the Hausdorff distance a properly normalized random projection of $[-1,1]^n$ onto $\mathbb{R}^d$…