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Alexander: Traces of Semigroups Associated with Interacting Particle Systems
"... gemeinschaft getragenen Sonderforschungsbereiches 611 an der Universität Bonn entstanden und als Manuskript vervielfältigt worden. Bonn, Februar 2006 Traces of semigroups associated with interacting particle systems ..."
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gemeinschaft getragenen Sonderforschungsbereiches 611 an der Universität Bonn entstanden und als Manuskript vervielfältigt worden. Bonn, Februar 2006 Traces of semigroups associated with interacting particle systems
Equilibrium Kawasaki dynamics of continuous particle systems
 INFIN. DIMENS. ANAL. QUANTUM PROBAB. RELAT. TOP
, 2007
"... We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the a prior ..."
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We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the a priori explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birthanddeath process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).
Analysis on Configuration Spaces and Gibbs Cluster Ensembles
, 2007
"... The distribution µ of a Gibbs cluster point process in X = R d (with npoint clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in X × X n. We show that µ is quasiinvariant with respect to the group Diff0(X) of compactly supported diffeomorp ..."
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Cited by 4 (0 self)
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The distribution µ of a Gibbs cluster point process in X = R d (with npoint clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in X × X n. We show that µ is quasiinvariant with respect to the group Diff0(X) of compactly supported diffeomorphisms of X and prove an integrationbyparts formula for µ. The corresponding equilibrium stochastic dynamics is then constructed by using the method of Dirichlet forms.
Laplace operators in deRham complexes associated with measures on configuration spaces
, 2001
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Department of Mathematics PREPRINT SERIES 2011/2012 NO: 5 TITLE: ‘CLUSTER POINT PROCESSES ON MANIFOLDS’
"... The probability distribution µcl of a general cluster point process in a Riemannian manifold X (with independent random clusters attached to points of a configuration with distribution µ) is studied via the projection of an auxiliary measure ˆµ in the space of configurations ˆγ = {(x, ¯y)} ⊂ X × X, ..."
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The probability distribution µcl of a general cluster point process in a Riemannian manifold X (with independent random clusters attached to points of a configuration with distribution µ) is studied via the projection of an auxiliary measure ˆµ in the space of configurations ˆγ = {(x, ¯y)} ⊂ X × X, where x ∈ X indicates a cluster “centre” and ¯y ∈ X: = ⊔ nXn represents a corresponding cluster relative to x. We show that the measure µcl is quasiinvariant with respect to the group Diff0(X) of compactly supported diffeomorphisms of X, and prove an integrationbyparts formula for µcl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. General constructions are illustrated by examples including Euclidean spaces, Lie groups, homogeneous spaces, Riemannian manifolds and metric spaces. The paper is an extension of our earlier results for Poisson cluster measures [J. Funct. Analysis 256 (2009) 432–478] and for Gibbs cluster measures
Measures on twocomponent configuration spaces∗
"... We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we show that a support set for the such Gibbs measure is the set ..."
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We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we show that a support set for the such Gibbs measure is the set of pairs of nonintersected configurations. MSC Classification: 82B21, 28A35
Condensed Matter Physics,????, Vol.?, No?(??), pp. 1–?? Selectionmutation balance models with epistatic selection
, 2008
"... We present an application of birthanddeath processes on configuration spaces to a generalized mutationselection balance model. The model describes aging of a population as a process of accumulation of mutations in a genotype. A rigorous treatment demands that mutations correspond to points in abs ..."
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We present an application of birthanddeath processes on configuration spaces to a generalized mutationselection balance model. The model describes aging of a population as a process of accumulation of mutations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. Our model describes an infinitepopulation, infinitesites model in continuum. The dynamical equation which describes the system, is of KimuraMaruyama type. The problem can be posed in terms of evolution of states (differential equation) or, equivalently, represented in terms of FeynmanKac formula. The questions of interest are existence of a solution, its asymptotic behavior, and properties of the limiting state. In the nonepistatic case the problem was posed and solved in [D. Steinsaltz, S.N. Evans, and Wachter K.W., Adv. Appl. Math., 35(1), 2005]. In our model we consider a topological space X as the space of positions of mutations and the influence of an epistatic potential.
Random Witten Laplacians: Traces of
, 2006
"... Diese Arbeit ist mit Unterstützung des von der Deutschen Forschungsgemeinschaft getragenen Sonderforschungsbereiches 611 an der Univer ..."
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Diese Arbeit ist mit Unterstützung des von der Deutschen Forschungsgemeinschaft getragenen Sonderforschungsbereiches 611 an der Univer