The measure-theoretical approach to \(p\)-adic probability theory

DOI10.5802/ambp.112zbMath0941.60010OpenAlexW2085063588MaRDI QIDQ1301236

Shinichi Yamada, Andrei Yu. Khrennikov, Arnoud C. M. van Rooij

Publication date: 2 September 1999

Published in: Annales Mathématiques Blaise Pascal (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AMBP_1999__6_1_21_0

zbMATH Keywords

\(p\)-adic numbersnon-Archimedean measures\(p\)-adic probability formalismconditional expectations for \(p\)-adic valued random variablesformula of the change of variables

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Foundations of probability theory (60A99)

Related Items (28)

Hysteresis model of unconscious-conscious interconnection: exploring dynamics on \(m\)-adic trees ⋮ Chaos in p-adic Statistical Lattice Models: Potts Model ⋮ Unnamed Item ⋮ On periodic Gibbs measures of \(p\)-adic Potts model on a Cayley tree ⋮ Dynamics measured in a non-Archimedean field ⋮ On dynamical systems and phase transitions for \(q + 1\)-state \(p\)-adic Potts model on the Cayley tree ⋮ p-Adic valued logical calculi in simulations of the slime mould behaviour ⋮ A dynamical system approach to phase transitions for \(p\)-adic Potts model on the Cayley tree of order two ⋮ p$$ p $$‐Adic phase transitions for countable state Potts model ⋮ Construction of a set of \(p\)-adic distributions ⋮ \(p\)-adic Gibbs measures and Markov random fields on countable graphs ⋮ The \(p\)-adic Potts model on the Cayley tree of order three ⋮ \(p\)-adic boundary laws and Markov chains on trees ⋮ Phase transitions forp-adic Potts model on the Cayley tree of order three ⋮ On the strong phase transition for the one-dimensional countable statep-adic Potts model ⋮ Phase transition for thep-adic Ising–Vannimenus model on the Cayley tree ⋮ Onp-adic Ising–Vannimenus model on an arbitrary order Cayley tree ⋮ Phase transition and chaos: \(p\)-adic Potts model on a Cayley tree ⋮ On \(p\)-adic quasi Gibbs measures for \(q+1\)-state Potts model on the Cayley tree ⋮ Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures ⋮ Renormalization method in \(p\)-adic \(\lambda\)-model on the Cayley tree ⋮ A reader's comment on: ``Hysteresis model of unconscious-conscious interconnection: exploring dynamics on \(m\)-adic trees ⋮ On \(G_2\)-periodic quasi Gibbs measures of \(p\)-adic Potts model on a Cayley tree ⋮ On the existence of generalized Gibbs measures for the one-dimensional \(p\)-adic countable state Potts model ⋮ On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions ⋮ Formalization of Probabilities with Non-linearly Ordered Ranges ⋮ On infinite products of non-Archimedean measure spaces ⋮ On descriptions of all translation invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• p-adic quantum mechanics
• A random walk on \(p\)-adics -- the generator and its spectrum
• \(p\)-adic probability and an interpretation of negative probabilities in quantum mechanics.
• \(p\)-adic probability theory and its application: The principle of statistical stabilization of frequencies
• p-ADIC HILBERT SPACE REPRESENTATION OF QUANTUM SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM
• Mathematical methods of non-Archimedean physics
• Representations of the Weyl group in spaces of square integrable functions with respect top-adic valued Gaussian distributions
• \(p\)-adic probability interpretation of Bell's inequality

This page was built for publication: The measure-theoretical approach to \(p\)-adic probability theory