LIPIcs.APPROX-RANDOM.2017.29.pdf
- Filesize: 409 kB
- 10 pages
Document
Cutoff for a Stratified Random Walk on the Hypercube
Authors
-
Part of:
Volume:
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Randomization and Computation (RANDOM)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2017-08-11
File
Document Identifiers
Cite As Get BibTex
Anna Ben-Hamou and Yuval Peres. Cutoff for a Stratified Random Walk on the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 29:1-29:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.29
Abstract
We consider the random walk on the hypercube which moves by picking an ordered pair (i,j) of distinct coordinates uniformly at random and adding the bit at location i to the bit at location j, modulo 2. We show that this Markov chain has cutoff at time (3/2)n*log(n) with window of size n, solving a question posed by Chung and Graham (1997).
Subject Classification
Keywords
- Mixing times
- cutoff
- hypercube
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
-
Daniel Andrén, Lars Hellström, and Klas Markström. On the complexity of matrix reduction over finite fields. Advances in applied mathematics, 39(4):428-452, 2007.
-
Demetres Christofides. The asymptotic complexity of matrix reduction over finite fields. arXiv preprint arXiv:1406.5826, 2014.
-
Fan R. K. Chung and Ronald L. Graham. Stratified random walks on the n-cube. Random Structures and Algorithms, 11(3):199-222, 1997.
-
Persi Diaconis and Laurent Saloff-Coste. Walks on generating sets of abelian groups. Probability theory and related fields, 105(3):393-421, 1996.
-
Martin Kassabov. Kazhdan constants for SL_n(ℤ). International Journal of Algebra and Computation, 15(05n06):971-995, 2005.
-
D. A. Levin, Y. Peres, and E. L. Wilmer. Markov chains and mixing times. AMS, 2009.
-
Aikaterini Sotiraki. Authentication protocol using trapdoored matrices. PhD thesis, Massachusetts Institute of Technology, 2016.