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191004s2020 sz | o |||| 0|eng d |
| 005 |
20230829020308.1 |
| 020 |
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|a 9783030279684
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| 024 |
7 |
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|a 10.1007/978-3-030-27968-4
|2 doi
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| 035 |
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|a (DE-He213)978-3-030-27968-4
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| 050 |
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4 |
|a QA273.A1-274.9
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| 050 |
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|a QA274-274.9
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|a PBT
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|a MAT029000
|2 bisacsh
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|a PBT
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|a PBWL
|2 thema
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| 082 |
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|a 519.2
|2 23
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| 100 |
1 |
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|a Nachmias, Asaf.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 245 |
1 |
0 |
|a Planar Maps, Random Walks and Circle Packing :
|b École d'Été de Probabilités de Saint-Flour XLVIII - 2018 /
|c by Asaf Nachmias.
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| 250 |
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|a 1st ed. 2020.
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| 264 |
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1 |
|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2020.
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| 300 |
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|a 1 online resource (XII, 120 pages 36 illustrations, 8 illustrations in color.)
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
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| 347 |
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|a text file
|b PDF
|2 rda
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1 |
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|a École d'Été de Probabilités de Saint-Flour ;
|v 2243
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| 506 |
0 |
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|a Open Access
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| 520 |
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|a 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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| 650 |
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|a Probabilities.
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| 650 |
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|a Discrete mathematics.
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| 650 |
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|a Geometry.
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| 650 |
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|a Mathematical physics.
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| 650 |
1 |
4 |
|a Probability Theory and Stochastic Processes.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M27004
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| 650 |
2 |
4 |
|a Discrete Mathematics.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M29000
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| 650 |
2 |
4 |
|a Geometry.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M21006
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| 650 |
2 |
4 |
|a Mathematical Physics.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M35000
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| 655 |
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|a Electronic books.
|2 local
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| 710 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer Nature eBook
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| 776 |
0 |
8 |
|i Printed edition:
|z 9783030279677
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| 776 |
0 |
8 |
|i Printed edition:
|z 9783030279691
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| 830 |
|
0 |
|a École d'Été de Probabilités de Saint-Flour ;
|v 2243
|
| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-030-27968-4
|z Connect to the full text of this electronic book
|t 0
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| 950 |
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|a Mathematics and Statistics (SpringerNature-11649)
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| 950 |
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|a Mathematics and Statistics (R0) (SpringerNature-43713)
|
| 955 |
|
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|a Springer OA ebooks
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| 999 |
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|
| 952 |
f |
f |
|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e QA274-274.9
|h Library of Congress classification
|
| 998 |
f |
f |
|a QA274-274.9
|t 0
|l Available Online
|