Related papers: Generalised Markov numbers
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
We propose a generalization of Carmichael numbers, where the multiplicative group $\mathbb G_\mathrm{m} = \mathrm{GL}(1)$ is replaced by $\mathrm{GL}(m)$ for $m\geq 2$. We prove basic properties of these families of numbers and give some…
In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation over metric spaces under a suitable transversality condition…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
We consider generalized metric spaces taking distances in an arbitrary ordered commutative monoid, and investigate when a class $\mathcal{K}$ of finite generalized metric spaces satisfies the Hrushovski extension property: for any…
We extend the general stochastic matching model on graphs introduced in (Mairesse and Moyal, 2016), to matching models on multigraphs, that is, graphs with self-loops. The evolution of the model can be described by a discrete time Markov…
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…
It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…
In this work we generalize Polya urn schemes with possibly infinitely many colors and extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of representing the observed sequence of colors in terms a…
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
We apply recent bounds of the author (math.PR/0609224) for generalized Smirnov statistics to the distribution of integers whose prime factors satisfy certain systems of inequalities.
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.
This paper concerns the \textbf{abstract geometry of numbers}: namely the pursuit of certain aspects of geometry of numbers over a suitable class of normed domains. (The standard geometry of numbers is then viewed as geometry of numbers…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…