Related papers: Random point sets and their diffraction

Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…

There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a…

Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular…

A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous…

We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that…

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…

For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…

Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…

We consider a diffusion risk model where proportional reinsurance can be bought. In order to stabilise the surplus process, one tries to keep the drawdown, that is the difference of the surplus to its historical maximum, in an interval…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

We construct a pair of related diffusions on a space of interval partitions of the unit interval $[0,1]$ that are stationary with the Poisson-Dirichlet laws with parameters (1/2,0) and (1/2,1/2) respectively. These are two particular cases…

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…

We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…