{"id":190043,"date":"2013-10-20T00:00:00","date_gmt":"2013-10-22T18:07:08","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/mixing-times-for-constrained-spin-models\/"},"modified":"2016-08-10T07:18:02","modified_gmt":"2016-08-10T14:18:02","slug":"mixing-times-for-constrained-spin-models","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/mixing-times-for-constrained-spin-models\/","title":{"rendered":"Mixing times for constrained spin models"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Consider the following Markov chain on the set of all possible zero-one labelings of a rooted binary tree of depth L: At each vertex v independently, a proposed new label (equally likely to be 0 or 1) is generated at rate 1. The proposed update is accepted iff either v is a leaf or both children of v are labeled &#8220;0\u201d. A natural question is to determine the mixing time of this chain as a function of L. The above is just an example of a general class of chains in which the local update of a spin occurs only in the presence of a special (&#8220;facilitating&#8221;) configuration at neighboring vertices. Although the i.i.d. Bernoulli distribution remains a reversible stationary measure, the relaxation to equilibrium of these chains can be extremely complex, featuring dynamical phase transitions, metastability, dynamical heterogeneities and universal behavior. I will report on progress on the mixing times for these models.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the following Markov chain on the set of all possible zero-one labelings of a rooted binary tree of depth L: At each vertex v independently, a proposed new label (equally likely to be 0 or 1) is generated at rate 1. The proposed update is accepted iff either v is a leaf or both [&hellip;]<\/p>\n","protected":false},"featured_media":197942,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-190043","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/62Pis6JrxgQ","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190043\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197942"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=190043"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=190043"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=190043"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=190043"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=190043"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=190043"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=190043"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=190043"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=190043"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=190043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}