Related papers: Marked Gibbs point processes with unbounded intera…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We adopt the interpretability offered by a parametric, Hawkes-process-inspired conditional probability mass function for the marks and apply variational inference techniques to derive a general and scalable inferential framework for marked…
The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap…
In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a suitable nonsmooth critical point theory.
We consider several special cases of iterations of random i.i.d. linear functions with beta distributed fixed points that generate nested interval schemes when iterated in a backward direction, and ergodic Markov chains in the forward…
We prove that a Gibbs point process interacting via a finite-range, repulsive potential $\phi$ exhibits a strong spatial mixing property for activities $\lambda < e/\Delta_{\phi}$, where $\Delta_{\phi}$ is the potential-weighted connective…
Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the…
We consider the problem of counting lattice points contained in domains in $\mathbb{R}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit…
We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that,…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
The Hawkes process is a self-exciting sample point process. It has wide applications in finance, social networks, criminology, seismology, and many other fields. With the development of storage technology, data-driven models are attracting…
We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…
We study large time behavior of critical marked Hawkes processes and related branching particle systems. In case of marked Hawkes processes we assume that the kernel function has multiplicative form and the marks corresponding to the events…
We consider a general class of spin systems with potentially unbounded real-valued spins, defined via a single-site potential with super-Gaussian tails on general graphs, allowing for both short- and long-range interactions. This class…
The aim of this work is to provide further insight into the qualitative behavior of mechanical systems that are well described by Lennard-Jones type interactions on an atomistic scale. By means of $\Gamma$-convergence techniques, we study…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by L\'{e}vy motion and their finite and infinite superpositions. We…
We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…