On stochastic generation of ultrametrics in high-dimensional Euclidean spaces

DOI10.1134/S2070046614020046zbMath1315.60020arXiv1311.5094MaRDI QIDQ2263137

Alexander P. Zubarev

Publication date: 17 March 2015

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.5094

zbMATH Keywords

law of large numbersdisordered systemsultrametricsultrametric spacesrandom distributionshigh-dimensional Euclidean spacesultrametricity index

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Metric spaces, metrizability (54E35) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30)

Related Items (6)

Finding ultrametricity in data using topology ⋮ \(p\)-adic mathematical physics: the first 30 years ⋮ On the ultrametric generated by random distribution of points in Euclidean spaces of large dimensions with correlated coordinates ⋮ Communicability cosine distance: similarity and symmetry in graphs/networks ⋮ Ultrametricity indices for the Euclidean and Boolean hypercubes ⋮ On the logistic behaviour of the topological ultrametricity of data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The problem of radiation transport in the channels of a polysectional thermodynamic system
• On \(p\)-adic mathematical physics
• Some aspects of \(m\)-adic analysis and its applications to \(m\)-adic stochastic processes
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Replica symmetry breaking and the nature of the spin glass phase
• Growth rate for the expected value of a generalized random Fibonacci sequence
• p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes
• p-adic description of characteristic relaxation in complex systems
• Application ofp-adic analysis to models of breaking of replica symmetry
• An Introduction to the Theory of Spin Glasses and Neural Networks
• Geometric Representation of High Dimension, Low Sample Size Data
• From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis

This page was built for publication: On stochastic generation of ultrametrics in high-dimensional Euclidean spaces