Related papers: Generalized Coverage Processes with Infinitely Div…
Occupied diffusions offer a Markovian framework for path-dependent dynamics by lifting the state space with a flow of occupation measures. Because this additional feature is infinite-dimensional, the simulation of these processes remains…
Let $X_1,X_2, \ldots $ and $Y_1, Y_2, \ldots$ be i.i.d. random uniform points in a bounded domain $A \subset \mathbb{R}^2$ with smooth or polygonal boundary. Given $n,m,k \in \mathbb{N}$, define the {\em two-sample $k$-coverage threshold}…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…
In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
In algebraic geometry there is a well-known categorical equivalence between the category of normal proper integral curves over a field $k$ and the category of finitely generated field extensions of $k$ of transcendence degree $1$. In this…
We introduce and investigate the notion of a $\mathbb Z$-graded covering for a supermanifold. More precisely, Donagi and Witten suggested a construction of the first obstruction class for splitting of a supermanifold via differential…
In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the…
We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…
Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus,…
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter Dirichlet…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of…