Exploring hypergraphs with martingales
Bollobás, Béla; Riordan, Oliver
- Recently, we adapted exploration and martingale arguments of Nachmias and Peres, in turn based on ideas of Martin-L$\backslash$"of, Karp and Aldous, to prove asymptotic normality of the number \$L\_1\$ of vertices in the largest component \$C\$ of the random \$r\$-uniform hypergraph throughout the supercritical regime. In this paper we take these arguments further to prove two new results: strong tail bounds on the distribution of \$L\_1\$, and joint asymptotic normality of \$L\_1\$ and the number \$M\_1\$ of edges of \$C\$.
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