Fluctuations of Interlacing Sequences
DOI:
https://doi.org/10.15407/mag13.04.364Анотація
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.
Ключові слова:
послідовності, що перемежовуються, проблема моментів Маркова, неперервні діаграми, випадкові матриці, центральна гранична теоремаПосилання
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