{"product_id":"9789814447522","title":"Random Walk In Random And Non-random Environments (Third Edition)","description":"\u003cp\u003eThe simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.\u003c\/p\u003e\u003cp\u003eSince the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSimple Symmetric Random Walk in ℤ\u003csup\u003e1\u003c\/sup\u003e:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction of Part I\u003c\/li\u003e\n\u003cli\u003eDistributions\u003c\/li\u003e\n\u003cli\u003eRecurrence and the Zero-One Law\u003c\/li\u003e\n\u003cli\u003eFrom the Strong Law of Large Numbers to the Law of Iterated Logarithm\u003c\/li\u003e\n\u003cli\u003eLévy Classes\u003c\/li\u003e\n\u003cli\u003eWiener Process and Invariance Principle\u003c\/li\u003e\n\u003cli\u003eIncrements\u003c\/li\u003e\n\u003cli\u003eStrassen Type Theorems\u003c\/li\u003e\n\u003cli\u003eDistribution of the Local Time\u003c\/li\u003e\n\u003cli\u003eLocal Time and Invariance Principle\u003c\/li\u003e\n\u003cli\u003eStrong Theorems of the Local Time\u003c\/li\u003e\n\u003cli\u003eExcursions\u003c\/li\u003e\n\u003cli\u003eFrequently and Rarely Visited Sites\u003c\/li\u003e\n\u003cli\u003eAn Embedding Theorem\u003c\/li\u003e\n\u003cli\u003eA Few Further Results\u003c\/li\u003e\n\u003cli\u003eSummary of Part I\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSimple Symmetric Random Walk in ℤ\u003csup\u003ed\u003c\/sup\u003e:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThe Recurrence Theorem\u003c\/li\u003e\n\u003cli\u003eWiener Process and Invariance Principle\u003c\/li\u003e\n\u003cli\u003eThe Law of Iterated Logarithm\u003c\/li\u003e\n\u003cli\u003eLocal Time\u003c\/li\u003e\n\u003cli\u003eThe Range\u003c\/li\u003e\n\u003cli\u003eHeavy Points and Heavy Balls\u003c\/li\u003e\n\u003cli\u003eCrossing and Self-crossing\u003c\/li\u003e\n\u003cli\u003eLarge Covered Balls\u003c\/li\u003e\n\u003cli\u003eLong Excursions\u003c\/li\u003e\n\u003cli\u003eSpeed of Escape\u003c\/li\u003e\n\u003cli\u003eA Few Further Problems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eRandom Walk in Random Environment:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction of Part III\u003c\/li\u003e\n\u003cli\u003eIn the First Six Days\u003c\/li\u003e\n\u003cli\u003eAfter the Sixth Day\u003c\/li\u003e\n\u003cli\u003eWhat Can a Physicist Say About the Local Time ξ(0,\u003ci\u003en\u003c\/i\u003e)?\u003c\/li\u003e\n\u003cli\u003eOn the Favourite Value of the RWIRE\u003c\/li\u003e\n\u003cli\u003eA Few Further Problems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eRandom Walks in Graphs:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction of Part IV\u003c\/li\u003e\n\u003cli\u003eRandom Walk in Comb\u003c\/li\u003e\n\u003cli\u003eRandom Walk in a Comb and in a Brush with Crossings\u003c\/li\u003e\n\u003cli\u003eRandom Walk on a Spider\u003c\/li\u003e\n\u003cli\u003eRandom Walk in Half-Plane-Half-Comb\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers in probability theory and statistical physics.\u003cbr\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47143946551536,"sku":"9789814447522","price":50.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814447522_p0.jpg?v=1763691012","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814447522","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}