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Asymptotics of large random strict plane partitions and generalized MacMahon's formula
Probability| Speaker: | Mirjana Vuletic, California Institute of Technology |
| Location: | 1147 MSB |
| Start time: | Wed, Dec 5 2007, 4:10PM |
Description
We introduce a measure on strict plane partitions that is an analog of the
uniform measure on plane partitions. We describe this measure in terms of
a Pfaffian point process and compute its bulk limit when partitions become
large.
The above measure is a special case of the shifted Schur process, which
generalizes the shifted Schur measure introduced by Tracy and Widom and is
an analog of the Schur process introduced by Okounkov and Reshetikhin. We
prove that the shifted Schur process is a Pfaffian point process and
calculate its correlation kernel.
Along the way we also obtain a one parameter generalization of Macmahon's
formula for the generating function of plane partitions.