A Meinardus theorem with multiple singularities
arXiv:1102.5608 · doi:10.1007/s00220-012-1526-8
Abstract
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size , when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journal
References in corpus (3)
Cited by in corpus (11)
- M2-branes and plane partitions
- A method of finding the asymptotics of q-series based on the convolution of generating functions
- Asymptotic degeneracies of M2-brane SCFTs
- A Central Limit Theorem for Integer Partitions into Small Powers
- Asymptotic enumeration by Khintchine-Meinardus method: Necessary and sufficient conditions for sub exponential growth
- Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration
- Supersymmetric zeta functions and determinants
- Explicit asymptotic formulae for sub exponentially growing multiplicative structures
- Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions
- A glimpse into the Ultrametric spectrum
- A Local Limit Theorem for Integer Partitions into Small Powers