Related papers: Interactions between Ehrenfest's urns arising from…
We introduce a modification of the generalized P\'olya urn model containing two urns and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$, $J\in\mathbb{N}$ added to the urns after $n$ draws. We provide sufficient…
The spectrum of a Gelfand pair of the form (K lx N, K), where N is a nilpotent group, can be embedded in a Euclidean space Rd . The identification of the spherical transforms of K-invariant Schwartz functions on N with the restrictions to…
This paper is a continuation of [8], in the direction of proving the conjecture that the spherical transform on a nilpotent Gelfand pair (N,K) establishes an isomorphism between the space of K-invariant Schwartz functions on N and the space…
Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generate interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Of great recent interest is the role these…
We introduce an urn model which describes spatial separation of sand. In this dynamical model, in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken. The…
In this article the zonal spherical functions of the Gelfand pair $(G(r,d,n), S_n)$ of complex reflection groups will be calculated. After this, a product formula for these spherical functions and a discrete analog of the Laplace operator…
In this article, using the notion of group contraction, we obtain the spherical functions of the strong Gelfand pair $(\mathrm{M}(n),\mathrm{SO}(n))$ as an appropriate limit of spherical functions of the strong Gelfand pair…
Axelrod's model describes the dissemination of a set of cultural traits in a society constituted by individual agents. In a social context, nevertheless, individual choices toward a specific attitude are also at the basis of the formation…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
This paper is a further investigation of the generalized $N$-urn Ehrenfest model introduced in \cite{Xue2020}. A moderate deviation principle from the hydrodynamic limit of the model is derived. The proof of this main result follows a…
We consider a coupled Polya's urn scheme for social dynamics on networks. Agents hold continuum-valued opinions on a two-state issue and randomly converse with their neighbors on a graph, agreeing on one of the two states. The probability…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…
Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady…
The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold $\theta$. The…
In order to find out whether there exists a thermodynamic description of the glass phase, the Ehrenfest relations along the glass transition line are reconsidered. It is explained that the one involving the compressibility is always…
We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators…
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Gallavotti-Spohn models. Under a suitable Boltzmann-Grad type…
We complete the study of the model introduced in [11]. It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the…
The Deffuant model is a spatial stochastic model for the dynamics of opinions in which individuals are located on a connected graph representing a social network and characterized by a number in the unit interval representing their opinion.…