Related papers: Poisson-process limit-laws yield Gumbel Max-Min an…
Consider n items located randomly on a circle of length 1. The locations of the items are assumed to be independent and uniformly distributed on [0,1). A picker starts at point 0 and has to collect all n items by moving along the circle at…
We show that a uniformly continuous random perturbation of a transitive map defines an aperiodic Harris chain which also satisfies Doeblin's condition. As a result, we get exponential decay of correlations for suitable random perturbations…
Motivated by applications in cybersecurity and epidemiology, we consider the problem of detecting an abrupt change in the intensity of a Poisson process, characterised by a jump (non transitory change) or a bump (transitory change) from…
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $\alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial…
Apriori Algorithm is one of the most important algorithm which is used to extract frequent itemsets from large database and get the association rule for discovering the knowledge. It basically requires two important things: minimum support…
Data separation is a well-studied phenomenon that can cause problems in the estimation and inference from binary response models. Complete or quasi-complete separation occurs when there is a combination of regressors in the model whose…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
This work defines and investigates the properties of the Max-U-Exp distribution. The method of moments is applied in order to estimate its parameters. Then, by using the previous general theory about Mixed Poisson processes, developed by…
The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks.…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is…
Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the…
Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the…
We consider a two-speed branching random walk, which consists of two macroscopic stages with different reproduction laws. We prove that the centered maximum converges in law to a Gumbel variable with a random shift and the extremal process…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements…
Place an $A$-particle at each site of a graph independently with probability $p$ and otherwise place a $B$-particle. $A$- and $B$-particles perform independent continuous time random walks at rates $\lambda_A$ and $\lambda_B$, respectively,…
Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in $R^d$. For a positive (respectively, negative) parameter $\gamma$ we consider red-blue matchings that locally minimize (respectively,…
We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line…