Systems in stochastic equilibrium
Systems in stochastic equilibrium
Random set partitions: asymptotics of subset counts
Journal of Combinatorial Theory Series A
The largest tree in certain models of random forests
proceedings of the eighth international conference on Random structures and algorithms
Random graphs
Ergodicity of multiplicative statistics
Journal of Combinatorial Theory Series A
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This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges at the radius of convergence; here, this property is expressed in terms of the expectations of independent random variables Zj, j ≥ 1, whose joint distribution, conditional on the event that Σnj=1 jZj = n, gives the distribution of the component spectrum for a random structure of size n. For a large class of such structures, we show that the component spectrum is asymptotically composed of Zj components of small sizes j, j ≥ 1, with the remaining part, of size close to n, being made up of a single, giant component.