Pseudo-mixing time of random walks

Itai Benjamini; Oded Goldreich

doi:10.1007/978-3-030-43662-9_20

Pseudo-mixing time of random walks

Itai Benjamini, Oded Goldreich

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We introduce the notion of pseudo-mixing time of a graph, defined as the number of steps in a random walk that suffices for generating a vertex that looks random to any polynomial-time observer. Here, in addition to the tested vertex, the observer is also provided with oracle access to the incidence function of the graph. Assuming the existence of one-way functions, we show that the pseudo-mixing time of a graph can be much smaller than its mixing time. Specifically, we present bounded-degree N-vertex Cayley graphs that have pseudo-mixing time t for any t(N)=ω(loglogN). Furthermore, the vertices of these graphs can be represented by string of length 2log₂N, and the incidence function of these graphs can be computed by Boolean circuits of size poly(logN).

Original language	English
Title of host publication	Computational Complexity and Property Testing
Subtitle of host publication	On the Interplay Between Randomness and Computation
Editors	Oded Goldreich
Publisher	Springer Nature Switzerland AG
Pages	363-373
Number of pages	11
ISBN (Electronic)	978-3-030-43662-9
ISBN (Print)	978-3-030-43661-2
DOIs	https://doi.org/10.1007/978-3-030-43662-9_20
State	Published - 1 Jan 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12050 LNCS
ISSN (Print)	0302-9743

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-43662-9_20

Cite this

Benjamini, I., & Goldreich, O. (2020). Pseudo-mixing time of random walks. In O. Goldreich (Ed.), Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation (pp. 363-373). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-43662-9_20

Benjamini, Itai ; Goldreich, Oded. / Pseudo-mixing time of random walks. Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation. editor / Oded Goldreich. Springer Nature Switzerland AG, 2020. pp. 363-373 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Benjamini, I & Goldreich, O 2020, Pseudo-mixing time of random walks. in O Goldreich (ed.), Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12050 LNCS, Springer Nature Switzerland AG, pp. 363-373. https://doi.org/10.1007/978-3-030-43662-9_20

Pseudo-mixing time of random walks. / Benjamini, Itai ; Goldreich, Oded.
Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation. ed. / Oded Goldreich. Springer Nature Switzerland AG, 2020. p. 363-373 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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Benjamini I , Goldreich O. Pseudo-mixing time of random walks. In Goldreich O, editor, Computational Complexity and Property Testing: On the Interplay Between Randomness and Computation. Springer Nature Switzerland AG. 2020. p. 363-373. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-43662-9_20