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Infinite wedge and random partitions

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arxiv math/9907127 v3 pith:3UUITVZG submitted 1999-07-20 math.RT math-phmath.COmath.MPmath.PR

Andrei Okounkov This is my paper · ORCID
classification math.RTmath-phmath.COmath.MPmath.PR
keywords partitionsfunctionsmeasureformularandomalg-geomauthorbloch
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Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure, see math.CO/9905032) and also show that these correlations functions are tau-functions for the Toda lattice hierarchy. Also we give a new proof of the formula due to Bloch and the author, see alg-geom/9712009, for the so called n-point functions of the uniform measure on partitions and comment on the local structure of a typical partition.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 294 citations worldwide. Full citation record

  1. Multicritical Scaling Limit of Shifted Schur Measure

    math.CO 2026-05 unverdicted novelty 7.0 of 10

    Under multicritical conditions the edge scaling limit of correlations for the shifted Schur measure converges to the higher-order Airy kernel determinant, demonstrating a Pfaffian-to-determinantal transition.

  2. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

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    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

  3. A Two-Color Lift of the Shifted $t$-Schur Measure

    math.PR 2026-07 unverdicted novelty 6.0 of 10

    Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.

  4. Quiver superconformal index and giant gravitons: asymptotics and expansions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.

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