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STATES ON THE CUNTZ ALGEBRAS AND p-ADIC RANDOM WALKS

Part of: Stochastic processes Selfadjoint operator algebras Basic hypergeometric functions Diophantine equations Normed linear spaces and Banach spaces; Banach lattices Special classes of linear operators

Published online by Cambridge University Press:  19 July 2011

P. E. T. JORGENSEN  and
A. M. PAOLUCCI
P. E. T. JORGENSEN
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52224, USA (email: palle-jorgensen@uiowa.edu)
A. M. PAOLUCCI*
Affiliation:
Max–Planck–Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany (email: paolucci@mpim-bonn.mpg.de)
*
✉For correspondence; e-mail: paolucci@mpim-bonn.mpg.de
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Abstract

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We study Markov measures and p-adic random walks with the use of states on the Cuntz algebras Op. Via the Gelfand–Naimark–Segal construction, these come from families of representations of Op. We prove that these representations reflect selfsimilarity especially well. In this paper, we consider a Cuntz–Krieger type algebra where the adjacency matrix depends on a parameter q ( q=1 is the case of Cuntz–Krieger algebra). This is an ongoing work generalizing a construction of certain measures associated to random walks on graphs.

Keywords

commutatorquantum theorysignal processingp-adic analysisHilbert spacespectrum

MSC classification

Secondary: 47B47: Commutators, derivations, elementary operators, etc. 60G35: Signal detection and filtering 33D50: Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 46C05: Hilbert and pre-Hilbert spaces 46L52: Noncommutative function spaces 11D88: $p$-adic and power series fields 33D80: Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 2 , April 2011 , pp. 197 - 211
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author (PJ) thanks the US NSF for partial support.

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