Journal title
Random Structures and Algorithms
DOI
10.1002/rsa.20678
Issue
3
Volume
50
Last updated
2024-04-23T12:01:33.287+01:00
Page
325-352
Abstract
Recently, in [Random Struct Algorithm 41 (2012), 441–450] we adapted exploration and martingale arguments of Nachmias and Peres [ALEA Lat Am J Probab Math Stat 3 (2007), 133–142], in turn based on ideas of Martin‐Löf [J Appl Probab 23 (1986), 265–282], Karp [Random Struct Alg 1 (1990), 73–93] and Aldous [Ann Probab 25 (1997), 812–854], to prove asymptotic normality of the number L1 of vertices in the largest component urn:x-wiley:10429832:media:rsa20678:rsa20678-math-0001 of the random r‐uniform hypergraph in the supercritical regime. In this paper we take these arguments further to prove two new results: strong tail bounds on the distribution of L1, and joint asymptotic normality of L1 and the number M1 of edges of urn:x-wiley:10429832:media:rsa20678:rsa20678-math-0002 in the sparsely supercritical case. These results are used in [Combin Probab Comput 25 (2016), 21–75], where we enumerate sparsely connected hypergraphs asymptotically.
Symplectic ID
458352
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Publication type
Journal Article
Publication date
23 Mar 2017