Cutoff for a Stratified Random Walk on the Hypercube

Authors Anna Ben-Hamou, Yuval Peres



PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2017.29.pdf
  • Filesize: 409 kB
  • 10 pages

Document Identifiers

Author Details

Anna Ben-Hamou
Yuval Peres

Cite AsGet 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).
Keywords
  • Mixing times
  • cutoff
  • hypercube

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. 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. Google Scholar
  2. Demetres Christofides. The asymptotic complexity of matrix reduction over finite fields. arXiv preprint arXiv:1406.5826, 2014. Google Scholar
  3. Fan R. K. Chung and Ronald L. Graham. Stratified random walks on the n-cube. Random Structures and Algorithms, 11(3):199-222, 1997. Google Scholar
  4. Persi Diaconis and Laurent Saloff-Coste. Walks on generating sets of abelian groups. Probability theory and related fields, 105(3):393-421, 1996. Google Scholar
  5. Martin Kassabov. Kazhdan constants for SL_n(ℤ). International Journal of Algebra and Computation, 15(05n06):971-995, 2005. Google Scholar
  6. D. A. Levin, Y. Peres, and E. L. Wilmer. Markov chains and mixing times. AMS, 2009. Google Scholar
  7. Aikaterini Sotiraki. Authentication protocol using trapdoored matrices. PhD thesis, Massachusetts Institute of Technology, 2016. Google Scholar