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Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects, however, for most…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
We provide a stochastic thermodynamic description across scales for $N$ identical units with all-to-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with…
The problem of base station cooperation has recently been set within the framework of Stochastic Geometry. Existing works consider that a user dynamically chooses the set of stations that cooperate for his/her service. However, this…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…
The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern $\mathbf{x}$ and a…
This paper is devoted to the detailed analysis of three-dimensional motions in $\mathbb{R}^3$ with orthogonal directions switching at Poisson times and moving with constant speed $c>0$. The study of the random position at an arbitrary time…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
The misanthrope process is a class of stochastic interacting particle systems, generalizing the simple exclusion process. It allows each site of the lattice to accommodate more than one particle. We consider a special case of the one…
Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…
We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…