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A sequential importance sampling algorithm for generating random graphs with prescribed degrees
, 2006
"... Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a ra ..."
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Cited by 22 (0 self)
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Random graphs with a given degree sequence are a useful model capturing several features absent in the classical ErdősRényi model, such as dependent edges and nonbinomial degrees. In this paper, we use a characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows surprisingly efficient sequential importance sampling. Applications are given, including simulating a biological network and estimating the number of graphs with a given degree sequence. 1. Introduction. Random
Recent Progress in Coalescent Theory
"... Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such ..."
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Cited by 17 (2 self)
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Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such as spin glass models. The emphasis is on recent work concerning in particular the connection of these processes to continuum random trees and spatial models such as coalescing random walks.
Rainbow hamilton cycles in random regular graphs
"... Abstract. A rainbow subgraph of an edgecoloured graph has all edges of distinct colours. A random dregular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to 1 as n → ∞, provided d ≥ 8. 1. ..."
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Cited by 6 (1 self)
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Abstract. A rainbow subgraph of an edgecoloured graph has all edges of distinct colours. A random dregular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to 1 as n → ∞, provided d ≥ 8. 1.
fleming.moments.tex Large Deviations and Moments for the Euler Characteristic of a Random Surface
, 902
"... Abstract: We study random surfaces constructed by glueing together N/k filled kgons along their edges, with all (N − 1)!! = (N − 1)(N − 3) · · ·3 · 1 pairings of the edges being equally likely. (We assume that lcm{2, k} divides N.) The Euler characteristic of the resulting surface is related to ..."
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Abstract: We study random surfaces constructed by glueing together N/k filled kgons along their edges, with all (N − 1)!! = (N − 1)(N − 3) · · ·3 · 1 pairings of the edges being equally likely. (We assume that lcm{2, k} divides N.) The Euler characteristic of the resulting surface is related to the number of cycles in a certain random permutation of {1,...,N}. Gamburd has shown that when 2 lcm{2, k} divides N, the distribution of this random permutation converges to that of the uniform distribution on the alternating group AN in the totalvariation distance as N → ∞. We obtain largedeviations bounds for the number of cycles that, together with Gamburd’s result, allow us to derive sharp estimates for the moments of the number of cycles. These estimates allow us to confirm certain cases of conjectures made by Pippenger and Schleich. 1.