相关论文: Coagulation--fragmentation duality, Poisson--Diric…

For $0<\alpha<1,$ and $\theta>-\alpha,$ let $(S^{-\alpha}_{\alpha,\theta+r})_{\{r\ge 0\}}$ denote an increasing(decreasing) sequence of variables forming a time inhomogeneous Markov chain whose marginal distributions are equivalent to…

We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…

We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…

We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let $F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of the masses present at time…

Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of `doubled kets' (i.e. mixing), and by tracing out part of a `doubled' two-system ket (i.e. dilation). Both…

Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…

Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…

We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…

We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…

We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions $PD(a,0)$. Precisely, let $s$ be a proper random…

We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…

We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs-type fragmentation tree with Aldous' beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm…

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…

Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…

We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a…

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…

Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

We introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The…

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…