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Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the…
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinatorics. The first application is quasi-polynomial bounds for a…
In this note we extend a theorem from [13] about uniform circle random coverings
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.
We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and Dewey (2002) and V\'azquez, Flammini, Maritan and Vespignani…
The hexahedron recurrence was introduced by R. Kenyon and R. Pemantle in the study of the double-dimer model in statistical mechanics. It describes a relationship among certain minors of a square matrix. This recurrence is closely related…
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some…
Multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We discuss the possible sources of these oscillations and their impact on our…
We give several applications of the thick distributional calculus. We consider homogeneous distributions, point source fields, and higher order derivatives of order $0.$
In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions.…
We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results…
We give an analogy between non-reversible Markov chains and electric networks much in the flavour of the classical reversible results originating from Kakutani, and later Kem\'eny-Snell-Knapp and Kelly. Non-reversibility is made possible by…
We obtain a simple direct derivation of the differential equation governing the entropy flow probability distribution function of a stochastic system first obtained by Lebowitz and Spohn. Its solution agrees well with the experimental…
A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) construction. A number of known…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.
Mechanical responses of soft particle packings to quasi-static deformations are determined by the microscopic restructuring of force-chain networks, where complex non-affine displacements of constituent particles cause the irreversible…