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О мультипликативных функционалах детерминантных процессов
Успехи математических наук. 2012. № т.67 выпуск 1 (403). С. 177-178.
Bufetov A. I.
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Russian
Bufetov A. I., Известия РАН. Серия математическая 2015 Т. 79 № 6 С. 18-64
В статье рассматриваются бесконечные аналоги детерминантных мер ...
Added: October 16, 2015
Bufetov A. I., Bulletin of Mathematical Sciences 2016 Vol. 6 No. 1 P. 163-172
A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, ...
Added: February 10, 2016
Bufetov A. I., Известия РАН. Серия математическая 2016 Т. 80 № 2 С. 16-32
The second paper in this series is devoted to the convergence of sequences of infinite determinantal measures, understood as the convergence of sequences of the corresponding finite determinantal measures. Besides the weak topology in the space of probability measures on the space of configurations, we also consider the natural immersion (defined almost surely with respect ...
Added: July 7, 2016
Bufetov A. I., Dymov A. V., International Mathematics Research Notices 2019 Vol. 2019 No. 1 P. 249-319
The main result of this paper is a functional limit theorem for the sine-process. In
particular, we study the limit distribution, in the space of trajectories, for the number
of particles in a growing interval. The sine-process has the Kolmogorov property and
satisfies the central limit theorem, but our functional limit theorem is very different
from the Donsker Invariance ...
Added: November 23, 2017
Borodin A., Olshanski G., Electronic Journal of Probability 2013 Vol. 75 P. 1-43
The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group. In another context, the Thoma cone appears as the set of parameters for totally positive, upper triangular Toeplitz matrices of infinite size.
The purpose of the paper is to construct a family ...
Added: November 16, 2013
Bufetov A. I., Dymov A. V., Osada H., Journal of the Mathematical Society of Japan 2019 Vol. 71 No. 2 P. 451-469
The logarithmic derivative of a point process plays a key role
in the general approach, due to the third author, to constructing
diffusions preserving a given point process.
In this paper we explicitly compute the logarithmic derivative for determinantal
processes on R with integrable kernels, a large class that includes
all ...
Added: November 23, 2017
Bufetov A. I., Electronic Research Announcements in Mathematical Sciences 2013 Vol. 20 P. 12-30
Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal point process and a convergent, but not integrable, multiplicative functional. Theorem 4.1, the main result announced in this ...
Added: February 20, 2013
Bufetov A. I., Qiu Y., Comptes Rendus Mathematique 2015 Vol. 353 No. 6 P. 551-555
We obtain explicit formulae, in the form of regularized multiplicative functionals related to certain Blaschke products, of the Radon–Nikodym derivatives between reduced Palm measures of all orders for determinantal point processes associated with a large class of weighted Bergman spaces on the disk. Our method also applies to determinantal point processes associated with weighted Fock ...
Added: October 15, 2015
Bufetov A. I., Qiu Y., Communications in Mathematical Physics 2017 Vol. 351 No. 1 P. 1-44
We study determinantal point processes on D induced by the reproducing kernels of generalized Bergman spaces. In the first case, we show that all reduced Palm measures of the same order are equivalent. The Radon–Nikodym derivatives are computed explicitly using regularized multiplicative functionals. We also show that these determinantal point processes are rigid in the ...
Added: March 14, 2017