Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts

@article{Bogachev2015UnifiedDO,
  title={Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts},
  author={Leonid V. Bogachev},
  journal={Random Structures \& Algorithms},
  year={2015},
  volume={47}
}
  • L. Bogachev
  • Published 14 November 2011
  • Mathematics
  • Random Structures & Algorithms
We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form ℱ(z)=∏ℓ=1∞ℱ0(zℓ) (which entails equal weighting among possible parts ℓ∈ℕ ). Under mild technical assumptions on the function H0(u)=ln(ℱ0(u)) , we show that the limit shape ω*(x) exists and is given by the equation y=γ−1H0(e−γx) , where γ2=∫01u−1H0(u) du . The wide class of partition measures covered by… 
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