Fluctuations of interlacing sequences

Sasha Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In a series of works published in the 1990s, Kerov put forth various applications of the circle of ideas centered at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral theory. We demonstrate on several examples that his approach is also adequate to study the uctuations about the limiting shape. In the random matrix setting, we compare two continual diagrams: one is constructed from the eigenvalues of the matrix and the critical points of its characteristic polynomial, whereas the second one is constructed from the eigenvalues of the matrix and those of its principal submatrix. The uctuations of the latter diagram were recently studied by Erdős and Schröder; we discuss the uctuations of the former, and compare the two limiting processes. For Plancherel random partitions, the Markov correspondence establishes the equivalence between Kerov's central limit theorem for the Young diagram and the Ivanov-Olshanski central limit theorem for the transition measure. We outline a combinatorial proof of the latter, and compare the limiting process with the ones of random matrices.

Original languageEnglish
Pages (from-to)364-401
Number of pages38
JournalJournal of Mathematical Physics, Analysis, Geometry
Issue number4
StatePublished - 2017


FundersFunder number
Horizon 2020 Framework Programme639305


    • Central limit theorem
    • Continual diagrams
    • Interlacing sequences
    • Markov moment problem
    • Random matrices


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