Related papers: Interlacing sequences resulting from an interval s…
Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has…
Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated…
We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the…
We prove a number of limiting distributions for statistics for unimodal sequences of positive integers by adapting a probabilistic framework for integer partitions introduced by Fristedt. The difficulty in applying the direct analogue of…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit interval. Some effort has been made recently to…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
Recently, many authors have investigated how various partition statistics distribute as the size of the partition grows. In this work, we look at a particular statistic arising from the recent rejuvenation of MacMahon's partition analysis.…
In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with a primality testing. For any prime n the n-th term in the…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…
An interference experiment with entangled particles is theoretically analyzed, where one of the entangled pair (particle 1) goes through a multi-slit before being detected at a fixed detector. In addition, one introduces a mechanism for…
With reference to a previous work, the problem of the experimental detection of non-causal synordination patterns between two series of physical events is examined. It is necessary that the patterns in question act in a reproducible, or at…
We construct an easily described family of partitions of the positive integers into $n$ disjoint sets with essentially the same structure for every $n \geq 2$. In a special case, it interpolates between the Beatty $\frac{1}{\phi} +…