{"product_id":"two-dimensional-random-walk-serguei-popov-9781108459693","title":"Two-Dimensional Random Walk: From Path Counting to Random Interlacements","description":"The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Serguei Popov\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1108459692\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781108459693\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/18\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 200\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.67lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.47d\u003cbr\u003e\u003cbr\u003e\u003cb\u003eReview Citation(s): \u003c\/b\u003e\u003cbr\u003e\u003ci\u003eChoice\u003c\/i\u003e 08\/01\/2022","brand":"Serguei Popov","offers":[{"title":"Paperback","offer_id":43942934446335,"sku":"9781108459693","price":46.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_0fc293ac-1dfd-47e7-9d61-9bdba4da1631.jpg?v=1681495221","url":"https:\/\/www.whiterainbookhouse.com\/products\/two-dimensional-random-walk-serguei-popov-9781108459693","provider":"WR Book House","version":"1.0","type":"link"}