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We introduce a multi-species lattice gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargoes being carried by…
We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid $F^+$ in noncommutative probability spaces. We show that a partially spreadable…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
Let us consider a two-sided multi-species stochastic particle model with finitely many particles on $\mathbb{Z}$ defined as follows. Suppose that each particle is labelled by a positive integer $l$ and waits a random time exponentially…
Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…
This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed…
We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the $q$-oscillator valued six-vertex model on $m \times n$ square lattice. By invoking the…
In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
For an infinite system of particles arriving in and departing from a habitat $X$ -- a locally compact Polish space with a positive Radon measure $\chi$ -- a Markov process is constructed in an explicit way. Along with its location $x\in X$,…
We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as…
We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in…
We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic $R$ matrices of quantum affine algebra $U_q (A^{(1)}_n)$, matrix product construction of…
We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
Based on direct numerical simulations with point-like inertial particles, with Stokes numbers, $\textrm{St}=0, 0.5$, $3$, and $6$, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time…
We study a family of Markov processes on $\mathcal{P}^{(k)}$, the space of partitions of the natural numbers with at most $k$ blocks. The process can be constructed from a Poisson point process on…
Phase-type distribution has been an important probabilistic tool in the analysis of complex stochastic system evolution. It was introduced by Neuts \cite{Neuts1975} in 1975. The model describes the lifetime distribution of a finite-state…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…