Related papers: Two-parameter Poisson-Dirichlet measures and rever…
We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
The present paper provides a characterisation of exchangeable pairs of random measures $(\widetilde\mu_1,\widetilde\mu_2)$ whose identical margins are fixed to coincide with the distribution of a gamma completely random measure, and whose…
How much dependence is there in the prime factorization of a random integer distributed uniformly from 1 to n? How much dependence is there in the decomposition into cycles of a random permutation of n points? What is the relation between…
We show that a compound Poisson distribution holds for scaled exceedances of observables $\phi$ uniquely maximized at a periodic point $\zeta$ in a variety of two-dimensional hyperbolic dynamical systems with singularities $(M,T,\mu)$,…
It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and with reward, respectively. We first recall the…
The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized…
We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear…
We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…
We study the kinetics of diffusion-limited coalescence, A+A->A, and annihilation, A+A->0, in random media consisting of disconnected domains of reaction. Examples include excitons fusion and annihilation in porous matrices and along polymer…
The possibility of disappearance of the diffuse-intensity peak splitting induced by the Fermi surface (i.e., of coalescence of the intensity maxima) with decreasing temperature is predicted. The underlying mechanism is the compensation of…
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical…
Consider the diffusion process defined by the forward equation $u_t(t, x) = \tfrac{1}{2}\{x u(t, x)\}_{xx} - \alpha \{x u(t, x)\}_{x}$ for $t, x \ge 0$ and $-\infty < \alpha < \infty$, with an initial condition $u(0, x) = \delta(x - x_0)$.…
From the Poisson-Dirichlet diffusions to the $Z$-measure diffusions, they all have explicit transition densities. In this paper, we will show that the transition densities of the $Z$-measure diffusions can also be expressed as a mixture of…
In these expository notes, we describe some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. We use Pitman's proof of Cayley's formula, which proceeds via a calculation of the…
We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…
We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…
We establish scaling limit theorems for the up-down ordered Chinese restaurant processes (oCRPs) of Rogers and Winkel as processes in a space of interval partitions. As previously conjectured, the limits are self-similar diffusions…