Related papers: Convergence of multi-class systems of fixed possib…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
The multi-class prediction had gained popularity over recent years. Thus measuring fit goodness becomes a cardinal question that researchers often have to deal with. Several metrics are commonly used for this task. However, when one has to…
The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…
Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an…
We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely charactarized by a linear system of first order partial differential equations for one set of variables…
A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary…
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…
We study in this paper the large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multi-classes. The empirical vector is composed of local empirical measures characterizing the…
In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation,…
In statistical physics any given system can be either at an equilibrium or away from it. Networks are not an exception. Most network models can be classified as either equilibrium or growing. Here we show that under certain conditions there…
Every symbolic system supports a Borel measure that is invariant under the shift, but it is not known if every such systems supports a measure that is invariant under all of its automorphisms; known as a characteristic measure. We give…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…