Летняя математическая школа "Алгебра и геометрия"

Детерминантные процессы

Александр Буфетов (Université Aix-Marseille, МИАН, НИУ ВШЭ)

Видеозаписи лекций

• Лекция 1
• Лекция 2
• Лекция 3

Резюме

Determinantal point processes naturally appear in many problems of representation theory, asymptotic combinatorics and mathematical physics, especially, the theory of random matrices. They have recently become an extremely active area of research. The course will give an elementary introduction to determinantal point processes. Some open problems will be formulated.

Список литературы

1. А. Б. Сошников, Детерминантные случайные точечные поля,
   http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=321&option_lang=rus
2. Richard Kenyon, Lectures on Dimers,
   http://arxiv.org/abs/0910.3129
3. Russell Lyons, Determinantal probability: basic properties and conjectures,
   http://arxiv.org/abs/1406.2707
4. Alexei Borodin, Grigori Olshanski, Markov processes on partitions,
   http://arxiv.org/abs/math-ph/0409075
5. Kurt Johansson, Non-intersecting paths, random tilings and random matrices,
   http://arxiv.org/abs/math/0011250
6. Yanqi Qiu, Infinite random matrices and ergodic decomposition of finite or infinite Hua-Pickrell measures,
   http://arxiv.org/abs/1410.1167
7. Alexander I. Bufetov, Yanqi Qiu, Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions,
   http://ac.els-cdn.com/S1631073X1500093X/1-s2.0-S1631073X1500093X-main.pdf?_tid=c33d7978-3055-11e5-a143-00000aacb360&acdnat=1437558241_6464a63c307f12d1e604f9b6b5e99f08
8. Leonid Petrov, Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field,
   http://arxiv.org/abs/1206.5123
9. Leonid Petrov, Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes,
   http://arxiv.org/abs/1202.3901
10. В. Е. Горин, Непересекающиеся пути и ансамбль ортогональных многочленов Хана,
    http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=faa&paperid=2910&option_lang=rus
11. Alexander I. Bufetov, Infinite Determinantal Measures and The Ergodic Decomposition of Infinite Pickrell Measures,
    http://arxiv.org/abs/1312.3161
12. Alexander I. Bufetov, Quasi-symmetries of determinantal point processes,
    http://arxiv.org/abs/1409.2068