Bhamidi, S and Sen, SN (2020) Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees. In: Random Structures and Algorithms, 56 (3). pp. 676721.

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Abstract
We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (1) continuum scaling limits of uniform simple connected graphs with given degree sequence and asymptotics for the number of simple connected graphs with given degree sequence under some regularity conditions, and (2) scaling limits for the metric space structure of the maximal components in the critical regime of both the configuration model and the uniform simple random graph model with prescribed degree sequence under finite third moment assumption on the degree sequence. As a substantive application we answer a question raised by Ä�ernÃ½ and Teixeira study by obtaining the metric space scaling limit of maximal components in the vacant set left by random walks on random regular graphs.
Item Type:  Journal Article 

Publication:  Random Structures and Algorithms 
Publisher:  John Wiley and Sons Ltd 
Additional Information:  Copy right for this article belongs to Wiley 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  29 Sep 2020 10:59 
Last Modified:  29 Sep 2020 10:59 
URI:  http://eprints.iisc.ac.in/id/eprint/65045 
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