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Теорема существования предельных кривых для полиномиальных адических автоморфизмов.
Записки научных семинаров ПОМИ РАН. 2016. Т. 448. С. 177-200.
Minabutdinov A.
We prove existence of limiting curves (describing deviations in ergodic theorem) for cylindrical functions for Polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function we give necessary condition of a limiting curve to exist. Our work generalizes results by E'. Janvresse, T. de la Rue and Y. Velenik.
Klimenko A. V., Bufetov A., Series C., / Cornell University. Series math "arxiv.org". 2018. No. 1805.11743.
Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...
Added: September 18, 2018
Klimenko A. V., Буфетов А. И., Сириес К., Успехи математических наук 2020
В заметке представлен результат о сходимости почти всюду сферических средних для сохраняющщих вероятностную меру действий фуксовой группы, если группа и набор образующих удовлетворяют условию "ровных углов" (even corners). Именно, группа обладает фундаментальной областью, для которой граница замощения диска её образами состоит из целых геодезических, а в качестве набора образующих взяты элементы группы, переводящие эту фундаментальную ...
Added: October 31, 2019
Springer, 2013
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry. ...
Added: February 20, 2013
Blank M., Nonlinearity 2017 Vol. 30 No. 12 P. 4649-4664
The classical Birkhoff ergodic theorem in its most popular version says that the
time average along a single typical trajectory of a dynamical system is equal
to the space average with respect to the ergodic invariant distribution. This
result is one of the cornerstones of the entire ergodic theory and its numerous
applications. Two questions related to this subject ...
Added: July 16, 2018
Bufetov A., Klimenko A. V., Series C., Commentarii Mathematici Helvetici 2023 Vol. 98 No. 1 P. 41-134
We prove pointwise convergence of spherical averages for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen–Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...
Added: February 29, 2024
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2019 Т. 481 С. 74-86
A limiting curve of a stationary process in discrete time was defined by \'{E}. Janvresse, {T.} de~la Rue and {Y.} Velenik as the uniform limit
of the functions \[t\mapsto \big(S(tl_n) - tS(l_n)\big)/R_n \in C([0, 1]),\] where $S$ refers to the piecewise
linear extension of the partial sum, $R_n := \sup |S(tl_n) - tS(l_n))|$, and $(l_n) = (l_n(\omega))$ ...
Added: October 6, 2019
Minabutdinov A., Лодкин А. А., Записки научных семинаров ПОМИ РАН 2015 Т. 437 С. 145-183
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik on fluctuations in ergodic sums for the Pascal adic transformation in the case of any ergodic invariant measure and cylindric function. The result on non-discreteness of the spectrum of the Pascal adic is stated. ...
Added: October 14, 2015
Minabutdinov A., Journal of Mathematical Sciences 2017 Vol. 224 No. 2 P. 286-303
We prove the existence of and describe limiting curves resulting from deviations in the partial sums in the ergodic theorem for cylinder functions and polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by É. Janvresse, ...
Added: February 7, 2019
Minabutdinov A., Лодкин А. А., Манаев И. Е., / Санкт-Петербургское математическое общество. Серия MSP "Preprints of the St. Petersburg Mathematical Society". 2014. № 11.
The paper generalizes the results by \'E. Janvresse, T. de la Rue and Y. Velenik [22] and the work [9] of the third author on fluctuations in ergodic sums for the Pascal adic in the case of arbitrary ergodic invariant measures. In particular, we answer several questions from [22] and [9]. ...
Added: March 28, 2015
Blank M., [б.и.], 2017
We study typical points with respect to ergofic averaging of a general dynamical system. ...
Added: February 10, 2018
Minabutdinov A., Journal of Mathematical Sciences 2020 Vol. 247 No. 17 P. 688-695
A limiting curve of a stationary process in discrete time was defined by É. Janvresse, T. de la Rue, and Y. Velenik as the uniform limit of the certain renormalization of the process. We determine the limiting curves for the stationary sequence (f ∘ Tn(ω)) where T is the dyadic odometer and f is the weighted sum of digits ...
Added: November 21, 2020
V'yugin V., Theory of Computing Systems 2016 P. 403-423
We study a stability property of probability laws with respect to small violations of algorithmic randomness. Some sufficient
condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the
strong law of large numbers, the law of iterated logarithm, and even Birkhoff's pointwise ergodic theorem for ergodic
transformations, are stable in ...
Added: May 16, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2015 Т. 432 С. 224-260
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik [18] on fluctuations in ergodic sums for the Pascal adic transformation in the case of Lebesgue measure for a wide class of functions. In particular, we answer several questions from [18]. ...
Added: March 15, 2015
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022