Related papers: Automatic continuity of transversal distributions
We show that every ergodic dynamical system induces a system with pure Lebesgue spectrum of infinite multiplicity.
We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.
Absolute continuity implies uniform continuity, but generally not vice versa. In this short note, we present one sufficient condition for a uniformly continuous function to be absolutely continuous, which is the following theorem: For a…
We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…
We prove in three ways the basic fact of analysis that complex derivatives are continuous. The first, classical, proof of Cauchy and Goursat uses integration. The second proof of Whyburn and Connell is topological and is based on the…
We propose an algorithm for average consensus over a directed graph which is both fully asynchronous and robust to unreliable communications. We show its convergence to the average, while allowing for slowly growing but potentially…
We show that any finite-variance, isotropic random field on a compact group is necessarily mean-square continuous, under standard measurability assumptions. The result extends to isotropic random fields defined on homogeneous spaces where…
A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and…
We prove that, for an interval $X\subseteq \mathbb R$ and a normed space $Z$ diagonals of separately absolute continuous mappings $f:X^2\to Z$ are exactly such mappings \mbox{$g:X\to Z$} that there is a sequence $(g_n)_{n=1}^{\infty}$ of…
We consider continuous-time consensus systems whose interactions satisfy a form or reciprocity that is not instantaneous, but happens over time. We show that these systems have certain desirable properties: They always converge…
We prove that the spectrum of the discrete Schr\"odinger operator on $\ell^2(Z^2)$, $(\psi_{n,m})\mapsto -(\psi_{n+1,m} +\psi_{n-1,m} +\psi_{n,m+1} +\psi_{n,m-1})+V_n\psi_{n,m}$ is absolutely continuous.
We propose another proof of the high dimensional spectrum convergence of the weighted sample covariance, more concise and self-sufficient but with stronger, but reasonable assumptions. We explain and illustrates this theorem for different…
On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class including $\delta$- and weighted $\delta'$-couplings. Assuming the numbers of different edge…
Consider $(X_{i}(t))$ solving a system of $N$ stochastic differential equations interacting through a random matrix $\mathbf J = (J_{ij})$ with independent (not necessarily identically distributed) random coefficients. We show that the…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
We provide an illustration of a mechanism for Arnold's diffusion following a nonvariational approach and find explicit estimates for the diffusion time.
In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion,…
We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite…
We derive equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets. Our result generalizes previous results for classical semimartingales by replacing a strong uniqueness assumption by a weaker…
Divisibility monoids are a natural lattice-theoretical generalization of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the involved divisibility lattices is kept as an hypothesis, but the relations between the…