scholarly journals Volume Laws for Boxed Plane Partitions and Area Laws for Ferrers Diagrams

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Uwe Schwerdtfeger
Keyword(s):  
Uniform Distribution ◽  
Random Variables ◽  
Symmetry Class ◽  
Limit Laws ◽  
Plane Partitions ◽  
Symmetric Plane ◽  
International Audience ◽  
Ferrers Diagrams ◽  
Area Limit

International audience We asymptotically analyse the volume random variables of general, symmetric and cyclically symmetric plane partitions fitting inside a box. We consider the respective symmetry class equipped with the uniform distribution. We also prove area limit laws for two ensembles of Ferrers diagrams. Most limit laws are Gaussian.

scholarly journals Limit laws for a class of diminishing urn models.

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Markus Kuba ◽  
Alois Panholzer
Keyword(s):  
Random Variables ◽  
Urn Models ◽  
Limit Laws ◽  
Sampling Without Replacement ◽  
International Audience ◽  
Special Instance ◽  
Special Case

International audience In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by $M= \binom{ -a \,0}{c -d}, a,d∈\mathbb{N}$ and $c∈\mathbb{N} _0$. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case $a=c=d=1$. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, $a=d=1$ and $c=0$, and corresponding generalizations, $a,d∈\mathbb{N}$ and $c=0$.

scholarly journals The poset perspective on alternating sign matrices

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Jessica Striker
Keyword(s):  
Generating Function ◽  
Young Tableaux ◽  
Alternating Sign Matrices ◽  
Plane Partitions ◽  
Combinatorial Objects ◽  
Symmetric Plane ◽  
International Audience ◽  
Order Ideals ◽  
Nous Utilisons

International audience Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We put ASMs into a larger context by studying the order ideals of subposets of a certain poset, proving that they are in bijection with a variety of interesting combinatorial objects, including ASMs, totally symmetric self―complementary plane partitions (TSSCPPs), Catalan objects, tournaments, semistandard Young tableaux, and totally symmetric plane partitions. We use this perspective to prove an expansion of the tournament generating function as a sum over TSSCPPs which is analogous to a known formula involving ASMs. Les matrices à signe alternant (ASMs) sont des matrices carrées dont les coefficients sont 0,1 ou -1, telles que dans chaque ligne et chaque colonne la somme des entrées vaut 1 et les entrées non nulles ont des signes qui alternent. Nous incluons les ASMs dans un cadre plus vaste, en étudiant les idéaux des sous-posets d'un certain poset, dont nous prouvons qu'ils sont en bijection avec de nombreux objets combinatoires intéressants, tels que les ASMs, les partitions planes totalement symétriques autocomplémentaires (TSSCPPs), des objets comptés par les nombres de Catalan, les tournois, les tableaux semistandards, ou les partitions planes totalement symétriques. Nous utilisons ce point de vue pour démontrer un développement de la série génératrice des tournois en une somme portant sur les TSSCPPs, analogue à une formule déjà connue faisant appara\^ıtre les ASMs.

scholarly journals Tree-like tableaux

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Jean-Christophe Aval ◽  
Adrien Boussicault ◽  
Philippe Nadeau
Keyword(s):  
Insertion Procedure ◽  
International Audience ◽  
Ferrers Diagrams

International audience In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally on alternative and permutation tableaux. Our insertion procedure allows to define in particular two simple new bijections between tree-like tableaux and permutations: the first one is conceived specifically to respect the generalized pattern 2-31, while the second one respects the underlying tree of a tree-like tableau. Dans ce travail nous introduisons et étudions les tableaux boisés, qui sont certains remplissages de diagrammes de Ferrers en bijection simple avec les tableaux de permutation et les tableaux alternatifs. Nous décrivons une procédure d'insertion élémentaire sur nos tableaux qui donne une preuve limpide que les tableaux de taille n sont comptés par n!, et qui de plus respecte la plupart des statistiques standard sur les tableaux de permutation et tableaux alternatifs. Notre procédure d'insertion permet en particulier de définir deux nouvelles bijections simples entre tableaux et permutations: la première est conçue spécifiquement pour respecter le motif généralisé 2-31 sur les permutations, tandis que la deuxième respecte l'arbre binaire sous-jacent à un tableau boisé.

The distribution of the values of an entire function whose coefficients are independent random variables (II)

1995 ◽  
Vol 118 (3) ◽  
pp. 527-542 ◽  
Author(s):  
A. C. Offord
Keyword(s):  
Entire Function ◽  
Uniform Distribution ◽  
Entire Functions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Almost All

SummaryThis is a study of entire functions whose coefficients are independent random variables. When the space of such functions is symmetric it is shown that independence of the coefficients alone is sufficient to ensure that almost all such functions will, for large z, be large except in certain small neighbourhoods of the zeros called pits. In each pit the function takes every not too large value and these pits have a certain uniform distribution.

The limit behaviour of the maximum of random variables with applications to outlier-resistance

1984 ◽  
Vol 21 (03) ◽  
pp. 646-650 ◽  
Author(s):  
Rudolf Mathar
Keyword(s):  
Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Limit Laws ◽  
Underlying Distribution ◽  
Limit Behaviour

We consider degenerate limit laws for the sequence {Xn, n } n (N of successive maxima of identically distributed random variables. It turns out that the concentration of Xn, n for large n can be determined in terms of a tail ratio of the underlying distribution function F. Applications to the outlier-behaviour of probability distributions are given.

Limit laws for the maxima of a class of quasi-stationary sequences

1983 ◽  
Vol 20 (04) ◽  
pp. 814-821 ◽  
Author(s):  
K. F. Turkman ◽  
A. M. Walker
Keyword(s):  
Random Variables ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Stationary Sequences ◽  
Limiting Distributions ◽  
Limit Laws

A class of quasi-stationary sequences of random variables is introduced. After giving the definition, it is shown that the limiting distributions of the maxima of such sequences, when suitably normalized, converge to one of the three extreme-value distributions.

A remark on the central limit question for dependent random variables

1980 ◽  
Vol 17 (1) ◽  
pp. 94-101 ◽  
Author(s):  
Richard C. Bradley
Keyword(s):  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
Stable Limit ◽  
Limit Laws ◽  
Dependent Random Variables ◽  
Asymptotically Normal ◽  
Second Moments

Given a strictly stationary sequence {Xk, k = …, −1,0,1, …} of r.v.'s one defines for n = 1, 2, 3 …, . Here an example of {Xk} is given with finite second moments, for which Var(X1 + … + Xn)→∞ and ρ n → 0 as n→∞, but (X1 + … + Xn) fails to be asymptotically normal; instead there is partial attraction to non-stable limit laws.

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