Results 1  10
of
12
Asymptotic counting of BPS operators in superconformal field theories
, 2008
"... We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For nonzero coupling, the corresponding multivariable partition functions can be written in terms of generating functions for vector partitions or their weighted generali ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For nonzero coupling, the corresponding multivariable partition functions can be written in terms of generating functions for vector partitions or their weighted generalisations. We derive asymptotics for the density of states for a wide class of such multivariable partition functions. We also point out a particular factorisation property of the finite N partition functions. Finally, we discuss the concept of a limit curve arising from the large N partition functions, which is related to the notion of a “typical state” and discuss some implications for the holographic duals.
Ergodicity of multiplicative statistics
, 2008
"... For a subfamily of multiplicative measures on integer partitions we give conditions for associated Young diagrams to converge in probability after a proper rescaling to a certain curve named the limit shape of partitions. We provide explicit formulas for the scaling function and the limit shape cove ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
For a subfamily of multiplicative measures on integer partitions we give conditions for associated Young diagrams to converge in probability after a proper rescaling to a certain curve named the limit shape of partitions. We provide explicit formulas for the scaling function and the limit shape covering some known and some new examples.
Limit Theorems for the Number of Parts in a Random Weighted Partition
"... Let cm,n be the number of weighted partitions of the positive integer n with exactly m parts, 1 ≤ m ≤ n. For a given sequence bk,k ≥ 1, of part type counts (weights), the bivariate generating function of the numbers cm,n is given by the infinite product ∏∞ k=1 (1−uzk) −bk. Let D(s) = ∑∞ k=1 bkk−s,s ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Let cm,n be the number of weighted partitions of the positive integer n with exactly m parts, 1 ≤ m ≤ n. For a given sequence bk,k ≥ 1, of part type counts (weights), the bivariate generating function of the numbers cm,n is given by the infinite product ∏∞ k=1 (1−uzk) −bk. Let D(s) = ∑∞ k=1 bkk−s,s = σ+iy, be the Dirichlet generating series of the weights bk. In this present paper we consider the random variable ξn whose distribution is given by P(ξn = m) = cm,n/ ( ∑n m=1 cm,n),1 ≤ m ≤ n. We find an appropriate normalization for ξn and show that its limiting distribution, as n → ∞, depends on properties of the series D(s). In particular, we identify five different limiting distributions depending on different locations of the complex halfplane in which D(s) converges. 1 Introduction and Statement of the Results
Developments in the KhintchineMeinardus probabilistic method for asymptotic enumeration
"... A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler’s generating function k=1 S(z k) for partitions, where S(z) = (1 − z ..."
Abstract
 Add to MetaCart
(Show Context)
A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler’s generating function k=1 S(z k) for partitions, where S(z) = (1 − z)−1. By applying a method due to Khintchine, we extend Meinardus ’ theorem to find the asymptotics of the Taylor coefficients of generating functions of the form k=1 S(akz k)bk for sequences ak, bk and general S(z). We also reformulate the hypotheses of the theorem in terms of the above generating functions. This allows novel applications of the method. In particular, we prove rigorously the asymptotics of Gentile statistics and derive the asymptotics of combinatorial objects with distinct components.
Sampling Parts of Random Integer Partitions: A Probabilistic and Asymptotic Analysis
"... ar ..."
(Show Context)