{"595513":{"#nid":"595513","#data":{"type":"event","title":"ARC Colloquium: Reza Gheissari (NYU)","body":[{"value":"\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EAlgorithms \u0026amp; Randomness Center (ARC)\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EReza Gheissari (NYU)\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EMonday, October 2, 2017\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EKlaus 1116 East - 11:00 am\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ETitle:\u0026nbsp;\u003C\/strong\u003E\u003Cem\u003EMixing Times of Critical 2D Potts Models\u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThe Potts model is a generalization of the Ising model to $q\\geq 3$ states; on $\\mathbb Z^d$ it is an extensively studied model of statistical mechanics, known to exhibit a rich phase transition for $d=2$ at some $\\beta_c(q)$. Specifically, the Gibbs measure on $\\mathbb Z^2$ exhibits a sharp transition between a disordered regime when $\\beta\u0026lt;\\beta_c(q)$ and an ordered regime when $\\beta\u0026gt;\\beta_c(q)$. At $\\beta=\\beta_c(q)$, when $q\\leq 4$, the Potts model has a continuous phase transition and its scaling limit is believed to be conformally invariant; when $q\u0026gt;4$, the phase transition is discontinuous and the ordered and disordered phases coexist. \u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EI will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat-bath\/Metropolis) for the 2D Potts model, where the mixing time on an $n\\times n$ torus should transition from $O(\\log n)$ at high temperatures to exponential in $n$ at low temperatures, via a critical slowdown at $\\beta=\\beta_c$ of $n^z$ when $q\\leq 4$ and exponential in $n$ when $q\u0026gt;4$.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E--------------------------------------\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Ca href=\u0022http:\/\/cims.nyu.edu\/~reza\/\u0022\u003ESpeaker\u0026#39;s Webpage\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003EVideos of recent talks are available at: \u003Ca href=\u0022https:\/\/smartech.gatech.edu\/handle\/1853\/46836\u0022\u003Ehttps:\/\/smartech.gatech.edu\/handle\/1853\/46836\u003C\/a\u003E\u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003E\u003Ca href=\u0022https:\/\/mailman.cc.gatech.edu\/mailman\/listinfo\/arc-colloq\u0022\u003EClick here to subscribe to the seminar email list: arc-colloq@cc.gatech.edu \u003C\/a\u003E\u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Mixing Times of Critical 2D Potts Models (Klaus 1116 East at 11am)"}],"uid":"27544","created_gmt":"2017-09-05 19:20:34","changed_gmt":"2017-09-25 16:36:55","author":"Francella Tonge","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2017-10-02T12:00:00-04:00","event_time_end":"2017-10-02T13:00:00-04:00","event_time_end_last":"2017-10-02T13:00:00-04:00","gmt_time_start":"2017-10-02 16:00:00","gmt_time_end":"2017-10-02 17:00:00","gmt_time_end_last":"2017-10-02 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"70263","name":"ARC"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003E\u003Ca href=\u0022mailto:ftonge3@cc.gatech.edu\u0022\u003Eftonge3@cc.gatech.edu\u003C\/a\u003E\u003C\/p\u003E\r\n","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}