3 years ago

Mixing time of the Chung--Diaconis--Graham random process. (arXiv:2003.08117v1 [math.PR])

Sean Eberhard, Péter P. Varjú

Define on by , where the steps are chosen independently at random from . The mixing time of this random walk is known to be at most for almost all odd (Chung--Diaconis--Graham, 1987), and at least (Hildebrand, 2008). We identify a constant such that the mixing time is for almost all odd .

In general, the mixing time of the Markov chain modulo , where is a fixed positive integer and the steps are i.i.d. with some given distribution in , is related to the entropy of a corresponding self-similar Cantor-like measure (such as a Bernoulli convolution). We estimate the mixing time up to a factor whenever the entropy exceeds .

Publisher URL: http://arxiv.org/abs/2003.08117

DOI: arXiv:2003.08117v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.