Fluctuations of Interlacing Sequences

Автор(и)

  • Sasha Sodin Tel Aviv University, School of Mathematical Sciences, Tel Aviv, 69978, Israel
    Queen Mary University of London, School of Mathematical Sciences, London E1 4NS, United Kingdom

DOI:

https://doi.org/10.15407/mag13.04.364

Ключові слова:

послідовності, що перемежовуються, проблема моментів Маркова, неперервні діаграми, випадкові матриці, центральна гранична теорема

Анотація

У циклi робiт, опублікованих наприкiнцi 1990-х, Керов указав низку застосувань розв’язання проблеми моментiв Маркова та сумiжних з ним iдей до опису граничної форми континуальних дiаграм, що виникають у теорiї зображень та в спектральнiй теорiї. Ми демонструємо на кiлькох прикладах, що пiдхiд Керова придатний i для опису флуктуацiї навколо граничної форми.

Перший приклад вiдноситься до теорiї випадкових матриць. Ми порiвнюємо двi континуальнi дiаграми: перша будується за власними значеннями випадкової матрицi та критичними точками її характеристичного многочлена, а друга - за власними значеннями випадкової матрицi та її головної пiдматрицi. Флуктуацiї першої були описанi Ердешем i Шрьодером; ми описуємо флуктуацiї другої, i порiвнюємо граничнi гаусовi процеси.

Потiм ми розглядаємо випадковi дiаграми, розподiленi за мiрою Планшереля. Перетворення Маркова дозволяє встановити еквiвалентнiсть мiж центральною граничною теоремою Керова (яка описує флуктуацiї дiаграми) i центральною граничною теоремою Iванова-Ольшанського (яка описує флуктуацiї перехiдної мiри). Ми накреслюємо комбiнаторне доведення останньої теореми, а також порiвнюємо граничнi процеси з вiдповiдними процесами в теорiї випадкових матриць.

Mathematics Subject Classification: 60B20, 34L20, 05E10, 60F05, 44A60.

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Sodin, S. Fluctuations of Interlacing Sequences. Журн. мат. фіз. анал. геом. 2017, 13, 364-401.

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