Results 11  20
of
53
Ranked fragmentations
 ESAIM P&S
"... distributions for random partitions generated by a ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
(Show Context)
distributions for random partitions generated by a
Random mappings, forests, and subsets associated with AbelCayleyHurwitz multinomial expansions
, 2001
"... ..."
Asymptotic distributions for the cost of linear probing hashing
 RANDOM STRUCTURES AND ALGORITHMS
, 2001
"... We study moments and asymptotic distributions of the construction cost, measured as the total displacement, for hash tables using linear probing. Four different methods are employed for different ranges of the parameters; together they yield a complete description. This extends earlier results by F ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
We study moments and asymptotic distributions of the construction cost, measured as the total displacement, for hash tables using linear probing. Four different methods are employed for different ranges of the parameters; together they yield a complete description. This extends earlier results by Flajolet, Poblete and Viola. The average cost of unsuccessful searches is considered too.
A family of random trees with random edge lengths
, 1999
"... We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such asdegree sequence, shape, and total length are derived. An interpr ..."
Abstract

Cited by 12 (8 self)
 Add to MetaCart
(Show Context)
We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such asdegree sequence, shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random tree of Aldous and Pitman (1998). Key words and phrases. Continuum tree, enumeration, random tree, spanning tree, weighted tree, Cayley's multinomial expansion.
The cuttree of large GaltonWatson trees and the Brownian CRT. The Annals of Applied Probability
"... ar ..."
(Show Context)
AbelCayleyHurwitz multinomial expansions associated with random mappings, forests, and subsets
, 1998
"... Extensions of binomial and multinomial formulae due to Abel, Cayley and Hurwitz are related to the probability distributions of various random subsets, trees, forests, and mappings. For instance, an extension of Hurwitz's binomial formula is associated with the probability distribution of the r ..."
Abstract

Cited by 10 (9 self)
 Add to MetaCart
Extensions of binomial and multinomial formulae due to Abel, Cayley and Hurwitz are related to the probability distributions of various random subsets, trees, forests, and mappings. For instance, an extension of Hurwitz's binomial formula is associated with the probability distribution of the random set of vertices of a fringe subtree in a random forest whose distribution is defined by terms of a multinomial expansion over rooted labeled forests which generalizes Cayley's expansion over unrooted labeled trees. Contents 1 Introduction 2 Research supported in part by N.S.F. Grant DMS9703961 2 Probabilistic Interpretations 5 3 Cayley's multinomial expansion 11 4 Random Mappings 14 4.1 Mappings from S to S : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 4.2 The random set of cyclic points : : : : : : : : : : : : : : : : : : : : : : : 18 5 Random Forests 19 5.1 Distribution of the roots of a pforest : : : : : : : : : : : : : : : : : : : : 19 5.2 Conditioning on the set...
Pointed and multipointed partitions of type A and B
, 2005
"... The aim of this paper is to define and study pointed and multipointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As a corollary, we show that some operads are Koszul over Z. ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
(Show Context)
The aim of this paper is to define and study pointed and multipointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As a corollary, we show that some operads are Koszul over Z.
The Multinomial Distribution on Rooted Labeled Forests
, 1997
"... For a probability distribution (p s ; s 2 S) on a finite set S, call a random forest F of rooted trees labeled by S (with edges directed away from the roots) a pforest if given F has m edges the vector of outdegrees of vertices of F has a multinomial distribution with parameters m and (p s ; s 2 ..."
Abstract

Cited by 7 (7 self)
 Add to MetaCart
For a probability distribution (p s ; s 2 S) on a finite set S, call a random forest F of rooted trees labeled by S (with edges directed away from the roots) a pforest if given F has m edges the vector of outdegrees of vertices of F has a multinomial distribution with parameters m and (p s ; s 2 S), and given also these outdegrees the distribution of F is uniform on all forests with the given outdegrees. The family of distributions of pforests is studied, and shown to be closed under various operations involving deletion of edges. Some related enumerations of rooted labeled forests are obtained as corollaries. 1 Introduction Let F(S) denote the set of all forests of rooted trees labeled by a finite set S of size jSj. Each f 2 F(S) is a directed graph labeled by S, that is a subset of S \Theta S, such that each Research supported in part by N.S.F. Grant DMS9703961 connected component of the graph is a tree with edges directed away from some root vertex. The notation v f ...
Stationary Markov Processes Related To Stable OrnsteinUhlenbeck Processes And The Additive Coalescent
, 1998
"... We consider some classes of stationary, countingmeasurevalued Markov processes and their companions under timereversal. Examples arise in the LevyIto decomposition of stable OrnsteinUhlenbeck processes, the largetime asymptotics of the standard additive coalescent, and extreme value theory. T ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
We consider some classes of stationary, countingmeasurevalued Markov processes and their companions under timereversal. Examples arise in the LevyIto decomposition of stable OrnsteinUhlenbeck processes, the largetime asymptotics of the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support of the evolving countingmeasure are born or die randomly, but each point follows a deterministic flow during its lifetime.
The asymptotic behavior of the Hurwitz binomial distribution
 Combinatorics, Probability and Computing
, 1998
"... Hurwitz's extension of Abel's binomial theorem defines a probability distribution on the set of integers from 0 to n. This is the distribution of the number of nonroot vertices of a fringe subtree of a suitably defined random tree with n + 2 vertices. The asymptotic behaviour of this dist ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
Hurwitz's extension of Abel's binomial theorem defines a probability distribution on the set of integers from 0 to n. This is the distribution of the number of nonroot vertices of a fringe subtree of a suitably defined random tree with n + 2 vertices. The asymptotic behaviour of this distribution is described in a limiting regime where the distribution of the delabeled fringe subtree approaches that of a GaltonWatson tree with a mixed Poisson offspring distribution. 1 Introduction and statement of results Hurwitz [10] discovered the following identity of polynomials in n + 2 variables x; y and z s ; s 2 [n] := f1; : : : ; ng, which reduces to the binomial expansion of (x + y) n when Research supported in part by N.S.F. Grant DMS9703961 z s j 0: X A`[n] x(x + z A ) jAj\Gamma1 (y + z ¯ A ) j ¯ Aj = (x + y + z [n] ) n (1) where the sum is over all 2 n subsets A of [n], with the notations z A := P s2A z s , and jAj for the number of elements of A, and ¯ A := [n] \...