Markov property of determinantal processes with extended sine, Airy, and Bessel kernels

zbMath1259.82065arXiv1106.4360MaRDI QIDQ2906175

Hideki Tanemura, Makoto Katori

Publication date: 5 September 2012

Full work available at URL: https://arxiv.org/abs/1106.4360

zbMATH Keywords

random matrix theoryMarkov propertydeterminantal processesinfinite particle systemscorrelation kernelsentire function and topology

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Markov semigroups and applications to diffusion processes (47D07) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Random matrices (algebraic aspects) (15B52) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (12)

Interacting Brownian motions in infinite dimensions related to the origin of the spectrum of random matrices ⋮ Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group ⋮ Critical behavior of non-intersecting Brownian motions ⋮ Stochastic analysis of infinite particle systems—A new development in classical stochastic analysis and dynamical universality of random matrices ⋮ Strong Markov property of determinantal processes with extended kernels ⋮ Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials ⋮ Infinite-dimensional stochastic differential equations related to Bessel random point fields ⋮ Dynamical bulk scaling limit of Gaussian unitary ensembles and stochastic differential equation gaps ⋮ The logarithmic derivative for point processes with equivalent Palm measures ⋮ Markov dynamics on the dual object to the infinite-dimensional unitary group ⋮ Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions ⋮ Determinantal martingales and correlations of noncolliding random walks

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