Related papers: Distributions and wave front sets in the uniform n…
We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in non-Archimedean local fields whose characteristic is $0$ or sufficiently large. Our results together form a flexible framework for…
We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…
Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr\'e model with…
We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator…
In this paper we apply ideas from the theory of Uniform Distribution of sequences to Functional Analysis and then drawing inspiration from the consequent results, we study concepts and results in Uniform Distribution itself. So let $E$ be a…
We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$,…
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent…
A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Sch\"utzenberger gave a remarkable refinement and proved that these parameters are equi-distributed…
Let $f$ be a rational function of degree $d>1$ on the projective line over a possibly non-archimedean algebraically closed field. A well-known process initiated by Brolin considers the pullbacks of points under iterates of $f$, and produces…
We continue our study and applications of generalized H\"ormander spaces of distributions $\mathcal{D}'_{\gamma,\Lambda}$ with $C^\infty$ wavefront set included in a cone $\Lambda$ and the union of $H^s$-wave front sets in a second cone…
Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some of the difficulties related to ramification and small residue…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
Front propagation in a random environment is studied close to the depinning threshold. At zero temperature we show that the depinning force distribution exhibits a universal behavior. This property is used to estimate the velocity of the…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We prove results on the propagation of Gevrey and analytic wave front sets for a class of $C^\infty$ hypoelliptic equations with double characteristics.
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…