Related papers: Geometric Universality of Currents
At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached…
In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimum-spanning tree construction. We give closed form expressions for the average degree of…
A new generic dynamical phenomenon of pseudochaos and its relevance to the statistical physics both modern as well as traditional one are considered and explained in some detail. The pseudochaos is defined as a statistical behavior of the…
We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed…
The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and P\'olya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution…
In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…
Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…