Related papers: On the probability of a random lattice avoiding a …

We calculate the effect of two kinds of randomness on the hopping of an excitation through a nearly regular Rydberg gas. We present calculations for how fast the excitation can hop away from its starting position for different dimensional…

We prove the invariance principle for a \emph{random Lorentz-gas} particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass,…

Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant…

Let $\mu$ be a probability distribution on $\mathbb{R}^d$ which assigns measure zero to every hyperplane and $S$ a set of points sampled independently from $\mu$. What can be said about the expected combinatorial structure of the convex…

Let $n \in \mathbb{Z}_{\geq 3}.$ Given any Borel subset $A$ of $\mathbb{R}^n$ with finite and nonzero measure, we prove that the probability that the set of primitive points of a random full-rank unimodular lattice in $\mathbb{R}^n$ does…

A $d$-dimensional binary Markov random field on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, potentials $a=a(n)$ and $b=b(n)$ depend on $n$. Precise bounds for the probability for local configurations to…

We provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1 dimensional lattice and when $d\geq7$, we show…

We consider $p$-orientations, which are defined to be orientations of $d$-regular graphs such that every vertex either has in-degree $p$ or out-degree $p$. These generalise the orientations considered in Jaeger's conjecture, where $d=4p+1$.…

We present a numerical study for the threshold percolation probability, $p_c$, in the bond percolation model with multiple ranges, in the square lattice. A recent Theorem demonstrated by de Lima {\it et al.} [B. N. B. de Lima, R. P.…

Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…

We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the…

Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the…

Let $d\geq 3$ be a fixed integer and $A$ be the adjacency matrix of a random $d$-regular directed or undirected graph on $n$ vertices. We show there exist constants $\mathfrak d>0$, \begin{align*} {\mathbb P}(\text{$A$ is singular in…

Deformed relativistic kinematics, expected to emerge in a flat-spacetime limit of quantum gravity, predicts violation of discrete symmetries at energy scale in the vicinity of the Planck mass. Momentum-dependent deformations of the C, P and…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

We investigate the random flight process that arises as the Boltzmann-Grad limit of a random scatterer Lorentz gas with variable scatterer density in a gravitational field. For power function densities we show how the parameters of the…

Let $P_r(n)$ be the set of partitions of n with non negative rth differences. Let $\lambda$ be a partition chosen uniformly at random among the set $P_r(n)$. Let $d(\lambda)$ be a positive rth difference chosen uniformly at random in…

For a fixed degree sequence $\mathcal{D}=(d_1,...,d_n)$, let $G(\mathcal{D})$ be a uniformly chosen (simple) graph on $\{1,...,n\}$ where the vertex $i$ has degree $d_i$. In this paper we determine whether $G(\mathcal{D})$ has a giant…

Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex independently with probability p=c/n. We compute an explicit…

The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…