相关论文: Some aspects of additive coalescents
In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect…
The following article is one of introduction to additive frieze patterns, linking the subject to multiplicative frieze patterns. We also add two new theorems about additive frieze patterns (see theorem 2 and 5) and a conjecture about…
We introduce and analyze a novel type of coalescent processes called cross-multiplicative coalescent that models a system with two types of particles, $A$ and $B$. The bonds are formed only between the pairs of particles of opposite types…
With most of the focus to date having been on the coalescence of freely suspended droplets, much less is known about the coalescence of sessile droplets, especially in the case of droplets laden with surfactant. Here, we employ large-scale…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which…
A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on pre-wetted substrates has received little attention. Here, we experimentally…
Droplet coalescence is a common phenomenon and plays an important role in multi-disciplinary applications. Previous studies mainly consider the coalescence of miscible liquid, even though the coalescence of immiscible droplets on a solid…
We investigate the coalescence of surfactant-laden water droplets by using several different surfactant types and a wide range of concentrations by means of a coarse-grained model obtained by the statistical associating fluid theory. Our…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biolog-ical systems. The process of merging of liquid objects has been studied during the pastyears experimentally and theoretically in different geometries. We…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
The notion of degree and related notions concerning recurrence and transience for a class of L'evy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is examined with emphasis on the role of the…
We study a class of multitype branching L\'evy processes, where particles move according to type-dependent L\'evy processes, switch types via an irreducible Markov chain, and branch according to type-dependent laws. This framework…
Droplet coalescence is an important process in nature and various technologies (e.g. inkjet printing). Here, we unveil the surfactant mass-transport mechanism and report on several major differences in the coalescence of surfactant-laden…
We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic…
Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
The effects of Brownian motion on particle interactions with heterogeneous collectors are evaluated by adding stochastic Brownian displacements to the particle trajectories and comparing those trajectories to those where Brownian motion is…
Consider a population where individuals give birth at constant rate during their lifetimes to i.i.d. copies of themselves. Individuals bear clonally inherited types, but (neutral) mutations may happen at the birth events. The smallest…