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In the open circular billiard particles are placed initially with a uniform distribution in their positions inside a planar circular vesicle. They all have velocities of the same magnitude, whose initial directions are also uniformly…
Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
We consider a class of external potentials on the complex plane $\mathbb{C}$ for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We…
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk…
We introduce a L\'evy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers $\{\xi_i \}$ are independent random variables identically…
We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…
We consider the homogenization of a Poisson problem or a Stokes system in a randomly punctured domain with Dirichlet boundary conditions. We assume that the holes are spherical and have random centres and radii. We impose that the average…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
A simple method to calculate dispersion of the total number of droplets appeared in the process of nucleation caused by the smooth variation of external conditions has been presented. The analytical result for dispersion is compared with…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental…
Statistical agent-based models for crime have shown that repeat victimization can lead to predictable crime hotspots (see e.g. Short et al., Math. Models Methods Appl., 2008), then a recent study in one space dimension (Chaturapruek et al.,…
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right,…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…