Planar Maps, Random Walks and Circle Packing

Name: Planar Maps, Random Walks and Circle Packing
Brand: Springer Nature Switzerland AG
SKU: 9783030279677
Price: 49.03 EUR
Availability: InStock

École d'Été de Probabilités de Saint-Flour XLVIII - 2018

Autor: Asaf Nachmias

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer Nature Switzerland AG

Dostupnosť: Skladom u dodávateľa

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49.03 €

This open access book focuses on the interplay between random walks on planar maps and Koebe's circl...

Informácie o knihe

Autor

Asaf Nachmias

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2019

Stránok

120

EAN

9783030279677

Enbook ID

24519352

Vydavateľ

Springer Nature Switzerland AG

Hmotnosť

454

Rozmery

155 x 235 x 8

Kompletný popis

This open access book focuses on the interplay between random walks on planar maps and Koebe's circle packing theorem. Further topics covered include electric networks, the He-Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe's circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

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Planar Maps, Random Walks and Circle Packing

École d'Été de Probabilités de Saint-Flour XLVIII - 2018

Informácie o knihe

Kompletný popis

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Zákazníci, ktorí si kúpili túto knihu, kúpili tiež