Related papers: Locally uniform random permutations with large inc…

Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…

We consider the problem of estimating the Attention mechanism in small space, and prove the existence of coresets for it of nearly optimal size. Specifically, we show that for any set of unit-norm keys and values $(K,V)$ in $\mathbb{R}^d$,…

We study occurrences of patterns on clusters of size n in random fields on Z^d. We prove that for a given pattern, there is a constant a>0 such that the probability that this pattern occurs at most an times on a cluster of size n is…

We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…

For a permuton $\mu$ let $H_n(\mu)$ denote the Shannon entropy of the sampling distribution of $\mu$ on $n$ points. We investigate the asymptotic growth of $H_n(\mu)$ for a wide class of permutons. We prove that if $\mu$ has a non-vanishing…

We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point processes in the plane. This enables the use of geometric tools…

We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in {1,...,n} occurs k times, where k may depend on n. This generalizes the famous…

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…

Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…

A set $A$ of natural numbers possesses property $\mathcal{P}_h$, if there are no distinct elements $a_0,a_1,\dots ,a_h\in A$ with $a_0$ dividing the product $a_1a_2\dots a_h$. Erd\H{o}s determined the maximum size of a subset of…

For integers $g,m \geq 0$ and $n>0$, let $S_{g}(n,m)$ denote the graph taken uniformly at random from the set of all graphs on $\{1,2, \ldots, n\}$ with exactly $m=m(n)$ edges and with genus at most $g$. We use counting arguments to…

The paper is concerned with the equilibrium distribution $\Pi_n$ of the $n$-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a $(2+\a)$-th moment condition on the jump distributions, we…

Consider a uniform expanders family G_n with a uniform bound on the degrees. It is shown that for any p and c>0, a random subgraph of G_n obtained by retaining each edge, randomly and independently, with probability p, will have at most one…

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…

An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs. We connect this problem to the theory of permutation…

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…

We answer several questions of Erd\H{o}s regarding sequences of natural numbers $A$ whose translates $n+A$ intersect with the squarefree numbers in various specified ways. For instance, we show that if every translate only contains finitely…

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…

Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fraction expansions along the sequence {px: p\in S} approach…

Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of…