Related papers: Poisson-process limit-laws yield Gumbel Max-Min an…

Let $X_1,\ldots,X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density $f$. Under some conditions on $f$, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability…

A $d$-dimensional ferromagnetic Ising model on a lattice torus is considered. As the size of the lattice tends to infinity, two conditions ensuring a Poisson approximation for the distribution of the number of occurrences in the lattice of…

The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…

The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting…

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a…

The radial probability measures on $R^p$ are in a one-to-one correspondence with probability measures on $[0,\infty[$ by taking images of measures w.r.t. the Euclidean norm mapping. For fixed $\nu\in M^1([0,\infty[)$ and each dimension p,…

Kossovsky recently conjectured that the distribution of leading digits of a chain of probability distributions converges to Benford's law as the length of the chain grows. We prove his conjecture in many cases, and provide an interpretation…

We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for $\de$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with…

Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…

Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…

We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<=…

We consider a gossip network, consisting of $n$ nodes, which tracks the information at a source. The source updates its information with a Poisson arrival process and also sends updates to the nodes in the network. The nodes themselves can…

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

In this paper, we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical…

The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…

Consider a homogeneous Poisson point process in a compact convex set in $d$-dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point…

We implement the Ising model on a structural connectivity matrix describing the brain at a coarse scale. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information…