Related papers: Records in the Infinite Occupancy Scheme

We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…

We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line. We specify the distribution of the space of…

We consider a deposition model in which balls rain down at random towards a 2-dimensional surface, roll downwards over existing adsorbed balls, are adsorbed if they reach the surface, and discarded if not. We prove a spatial law of large…

An absorbing game is a stochastic game with a single nonabsorbing state. Such a game is called recursive if all players receive a payoff of 0 in the nonabsorbing state, and positive if all payoffs in absorbing states are positive. An action…

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

Consider a symmetrical conflict relationship between the points of a point process. The Mat\'ern type constructions provide a generic way of selecting a subset of this point process which is conflict-free. The simplest one consists in…

Let $P$ be a set of points and $L$ a set of lines in the (extended) Euclidean plane, and $I \subseteq P\times L$, where $i =(p,l) \in I$ means that point $p$ and line $l$ are incident. The incidences can be interpreted as quadratic…

Assume that $2n$ balls are thrown independently and uniformly at random into $n$ bins. We consider the unlikely event $E$ that every bin receives at least one ball, showing that $\Pr[E] = \Theta(b^n)$ where $b \approx 0.836$. Note that, due…

A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there…

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…

We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…

The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…

In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…

We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…

Let $(A_u : u \in \mathbb{B})$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $ \mathbb{B}$. Each car tries to park on its arrival node, but if it is already occupied, it drives…

We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…

Two Beatty sequences are recorded by athletes running in opposite directions in a round stadium. This approach suggests a nice interpretation for well known partitioning criteria: such sequences (eventually) partition the integers…

Let $r \in \mathbb{N}\cup\{\infty\}$ be a fixed number and let $P_j\,\, (1 \leq j\leq r )$ be the projection onto the closed subspace $\mathcal{M}_j$ of $\mathscr{H}$. We are interested in studying the sequence $P_{i_1}, P_{i_2}, \ldots…

Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…