Related papers: Expected Coalescence Time for a Nonuniform Allocat…
We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyam\'{e}-Galton-Watson process. Special interest is on the expected size of a…
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications…
We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices…
We come up with a class of distributed quantized averaging algorithms on asynchronous communication networks with fixed, switching and random topologies. The implementation of these algorithms is subject to the realistic constraint that the…
Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves.…
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial,…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations,…
We develop a full-fledged analysis of an algorithmic decision process that, in a multialternative choice problem, produces computable choice probabilities and expected decision times.
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
In this paper, we consider Galton-Watson processes with immigration. Pick $i(\ge2)$ individuals randomly without replacement from the $n$-th generation and trace their lines of descent back in time till they coalesce into $1$ individual in…
We propose in this article a brief description of the work, over almost a decade, resulting from a collaboration between mathematicians and biologists from four different research laboratories, identifiable as the co-authors of the articles…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each…
We discuss the time development of Gaussian wave packet solutions of the quantum bouncer' (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization…
While coalescence is ultimately the most drastic destabilization process in foams, its underlying processes are still unclear. To better understand them, we track individual coalescence events in two-dimensional foams at controlled…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss,…