Asymptotics and spectral results for random walks on \(p\)-adics

DOI10.1016/S0304-4149(99)00016-2zbMath0999.60072MaRDI QIDQ1613625

Witold Karwowski, Xue-Lei Zhao, Sergio A. Albeverio

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Dirichlet formsjump processesnull recurrenceMarkov processes on \(p\)-adic spacespectral properties of a generator on \(p\)-adic space

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Dirichlet forms (31C25) Algebraic number theory: local fields (11S99) Transition functions, generators and resolvents (60J35) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (17)

Measure-valued branching processes associated with random walks on \(p\)-adics. ⋮ Stable processes on the boundary of a regular tree ⋮ Sobolev space and Dirichlet space associated with symmetric Markov process on a local field ⋮ A class of spatially inhomogeneous Dirichlet spaces on the \(p\)-adic number field. ⋮ Stochastic Processes on Ends of Tree and Dirichlet Forms ⋮ Transitions on a noncompact Cantor set and random walks on its defining tree ⋮ Brownian motion and finite approximations of quantum systems over local fields ⋮ Random processes on non-Archimedean spaces ⋮ Transition semi-groups on a local field induced by Galois group and their representation ⋮ Time-inhomogeneous stochastic processes on the \(p\)-adic number field ⋮ Convergences and projection Markov property of Markov processes on ultrametric spaces ⋮ Transience and recurrence of random walks on percolation clusters in an ultrametric space ⋮ Removal of potential theoretic exceptional set on the field of \(p\)-adic numbers ⋮ \((r, p)\)-capacity and Hausdorff measure on a local field ⋮ Hausdorff dimension and hierarchical system dynamics ⋮ Jump processes on leaves of multibranching trees ⋮ Diffusion on locally compact ultrametric spaces.

Cites Work

• Introduction to the theory of (non-symmetric) Dirichlet forms
• Local field Brownian motion
• Dirichlet forms and symmetric Markov processes
• A random walk on \(p\)-adics -- the generator and its spectrum
• Random walk on \(p\)-adics with non-zero killing part
• Local properties of Lévy processes on a totally disconnected group
• A simple criterion for transience of a reversible Markov chain
• Random flights on regular graphs
• Continuity Properties of Gaussian Stochastic Processes Indexed by a Local Field
• Sample Path Properties of Gaussian Stochastic Processes Indexed by a Local Field
• Gibbs States on Countable Sets
• Isotropic random walks in a tree
• Hierarchical structures and asymmetric stochastic processes on p-adics and adeles
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