Random Combinatorial structures:the convergent case
| dc.creator | Barbour, A. D. | |
| dc.creator | Granovsky, B. | |
| dc.date | 2003-05-01 | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T08:06:07Z | |
| dc.date.available | 2026-07-07T08:06:07Z | |
| dc.description | 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 {\it independent} random variables $Z_j$, $j\ge1$, whose joint distribution, conditional on the event that $\sum_{j=1}^n jZ_j = n$, 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 $Z_j$ components of size $j$, $j\ge1$, with the remaining part, of size $n-\sum_{j\ge1} Z_j$, being made up of a single, giant component. | |
| dc.description | This the revised version that incorporates the referees remarks related mainly to the organization of the paper. The paper will be published in the J. of Combinatorial Theory, Ser.A | |
| dc.identifier | https://arxiv.org/abs/math/0305031 | |
| dc.identifier | http://arxiv.org/abs/math/0305031 | |
| dc.identifier | Journal of Combinatorial Theory, Series A 109(2005) 203-220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130499 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60G50,05A17,60K35,60F05,05A16 | |
| dc.title | Random Combinatorial structures:the convergent case | |
| dc.type | text |