Related papers: On a random model of forgetting

Let $A$ be an $n\times n$ random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large deviation inequality for the rank of $A$: for all $1\leq k\leq c\sqrt{n}$,…

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…

In this article, we show that a linear combination $X$ of $n$ independent, unbiased Bernoulli random variables $\{X_k\}$ can match the first $2n$ moments of a random variable $Y$ which is uniform on an interval. More generally, for each $p…

We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…

Suppose $(X_t)_{t \in T}$ is a Gaussian process indexed by some arbitrary set $T:$ the random variable $\sup_{t \in T}{X_t}$ can be very intricate and bounding its expectation is a natural step towards understanding it. Sudakov-Fernique…

In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…

The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…

We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number $N$ of harmonic oscillators.…

We analyze the asymptotic behavior of random variables $x(n,x\_0)$ defined by $x(0,x\_0)=x\_0$ and $x(n+1,x\_0)=A(n)x(n,x\_0)$, where $\sAn$ is a stationary and ergodic sequence of random matrices with entries in the semi-ring…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a…

Let S(1) be the segment [-1,1], and define the segments S(n) recursively in the following manner: let S(n+1) be the intersection of S(n) and a(n+1) + S(1), where the point a(n+1) is chosen randomly on the segment S(n) with uniform…

We outline basic properties of a symmetric random walk in one dimension, in which the length of the nth step equals lambda^n, with lambda<1. As the number of steps N-->oo, the probability that the endpoint is at x, P_{lambda}(x;N),…

We consider an ergodic process on finitely many states, with positive entropy. Our first main result asserts that the distribution function of the normalized waiting time for the first visit to a small (i.e., over a long block) cylinder set…

Let $S_n$ be the total gain in $n$ repeated St.\ Petersburg games. It is known that $n^{-1}(S_n-n\log_2n)$ converges in distribution to a random element $Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with…

We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…

Let $X_i,i=0,1,\ldots$ be a sequence of iid random variables whose distribution is continuous. Associated with this sequence is the sequence $(i,X_i),i=0,1,\ldots$. Let ${\cal R}_{n}$ denote the set of Pareto optimal elements of $\{…

We discuss an approach to compute the first and second moments of the number of eigenvalues $I_N$ that lie in an arbitrary interval of the real line for $N \times N$ Gaussian random matrices. The method combines the standard…

Let $X_1, X_2, \dots$ be independent, identically distributed random variables taking values from a compact metrizable group $G$. We prove that the random walk $S_k=X_1 X_2 \cdots X_k$, $k=1,2,\dots$ equidistributes in any given Borel…

Consider some convex body $K\subset\mathbb R^d$. Let $X_1,\dots, X_k$, where $k\leq d$, be random points independently and uniformly chosen in $K$, and let $\xi_k$ be a uniformly distributed random linear $k$-plane. We show that for…