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Finite graphs and amenability
Finite graphs amenability Functional Analysis
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2012/4/18
Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in compute...
Pseudodifferential operators on periodic graphs
Pseudodifferential operators periodic graphs Functional Analysis
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2011/9/21
Abstract: The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces on an infinite metric graph $\Gamma$ which is periodic with respect...
Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
Horizontal visibility graphs transformed fractional Brownian motions Topological properties versus Hurst index
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2010/12/28
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes.In recent years, quite a few methods have been proposed to transform a single time series to a comp...
Brownian Motions on Metric Graphs III - Construction: General Metric Graphs
Brownian motion metric graph Wentzell boundary condition
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2011/1/18
Consider a metric graph G with set of vertices V . Assume that for every vertex in V one is given a Wentzell boundary condition. It is shown how one can construct the paths of a Brownian motion on G s...
Brownian Motions on Metric Graphs II - Construction of Brownian Motions on Single Vertex Graphs
Brownian motion Feller Brownian motion metric graphs
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2011/1/18
Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of single vertex graphs are given.
Brownian Motions on Metric Graphs I - Definition, Feller Property, and Generators
Metric graphs Brownian motion Feller processes Feller’s theorem
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2011/1/18
Brownian motions on a metric graph are defined, their Feller property is proved, and their generators are characterized. This yields a version of Feller’s theorem for metric graphs.
Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
Pauli graphs Hilbert space dimension
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2010/12/9
We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.