{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Jeff Running","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/jeffrunn\/","title":"Anomalous Diffusion and Polya Recurrence - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"VeyVUbppC3\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/video\/anomalous-diffusion-and-polya-recurrence\/\">Anomalous Diffusion and Polya Recurrence<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/video\/anomalous-diffusion-and-polya-recurrence\/embed\/#?secret=VeyVUbppC3\" width=\"600\" height=\"338\" title=\"&#8220;Anomalous Diffusion and Polya Recurrence&#8221; &#8212; Microsoft Research\" data-secret=\"VeyVUbppC3\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/\/# sourceURL=https:\/\/www.microsoft.com\/en-us\/research\/wp-includes\/js\/wp-embed.min.js\n\/* ]]> *\/\n<\/script>\n","thumbnail_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/09\/A-64UjFSc8A.jpg","thumbnail_width":480,"thumbnail_height":360,"description":"After a brief introduction a survey of some recent results will be given of ergodic and stochastic properties of Sinai billiards. In particular, Polya\u2019s celebrated recurrence theorem, known to hold for planar random walks, is discussed for a deterministic model of Brownian motion which is defined via billiards."}