UNITED SEMINAR OF THE DEPARTMENT OF PROBABILITY THEORY OF LOMONOSOV MOSCOW STATE UNIVERSITY
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This is the page of the United Seminar of the Department of Probability Theory of the Faculty of Mechanics and Mathematics of Moscow State University. The permanent website of the seminar is here. The seminar is a continuation of the research seminar of the Department of Probability Theory under the leadership of A.N. Kolmogorov and B.V. Gnedenko.
The seminar is held online every Wednesday from 16:45 to 17:45 Moscow time.
Permanent link to the Zoom room: http://bit.ly/3HY8K6d
Room ID: 844 6792 3144 Access code: 697663
Head of the seminar: academician of the RAS, professor Albert N. Shiryaev
Coordinator of the seminar in spring 2025: professor Elena B. Yarovaya
Secretary of the seminar in spring 2025: Oleg E. Ivlev
To subscribe to the seminar newsletter or submit a talk, click "Subscribe or submit" at the top of the page.
We recommend you to study the network of seminars at this link, which were brought together by our colleagues from the Mathematical Center of the Southern Federal University.
The list of reports from 2020 and previous years can be viewed at this link.
The list of reports from 2021-2024 can be in the corresponding sections of this page.
We recommend you to study the network of seminars at this link, which were brought together by our colleagues from the Mathematical Center of the Southern Federal University.
The list of reports from 2020 and previous years can be viewed at this link.
The list of reports from 2021-2024 can be in the corresponding sections of this page.
Upcoming reports
Upcoming reports
May 14, 16:45 msk
Elena Lenena, Lomonosov MSU, Russia
Functional Limit Theorems for Queueing Networks in a Random Environment
The dissertation investigates generalized Jackson networks with regenerative input flows in a random environment. The main focus is on proving functional limit theorems: it establishes a strong approximation of the queue length vector by reflected Brownian motion in the positive orthant and derives explicit formulas for key parameters such as drift, reflection matrix, and covariance. The work provides estimates for deviation probabilities and the Wasserstein distance between the distributions of the processes. A method for estimating the covariance matrix in overloaded systems is developed. The dissertation addresses both theoretical aspects and practical examples, including transportation networks with unreliable components. The results are applicable to the analysis of stability, optimization, and diagnostics of complex service systems.
Past reports
Past reports
April 23, 16:45 msk
Alexander Bulinski, Lomonosov MSU, Russia
Contribution of mathematicians and mechanics to the victory in the Great Patriotic War
In our country, 2025 has been declared the Year of Defender of the Fatherland and the 80th anniversary of victory in the Great Patriotic War. We will consider the activities in the field of science and education that ensured the victory in this bloodiest war. The main focus is on the research of outstanding mathematicians and mechanics. These include A.A.Ilyushin, A.N.Kolmogorov, N.G.Chetaev, H.A.Rakhmatulin, A.N.Krylov, S.N.Bernstein, S.L.Sobolev, N.E.Kochin, M.V.Keldysh, M.A.Lavrentiev, S.A.Khristianovich and other scientists. The talk is dedicated to the victors of fascism.
The recording: YouTube
April 16, 16:45 msk
Tatyana Turova, Lund University, Sweden
Antiferromagnetic Covariance Structure of Coulomb Chain
We consider a system of particles lined up on a finite interval with 3-dimensional Coulomb interactions. Typically, models with interactions between all pairs of particles are studied. The main question of interest is the distribution of spacings between the consecutive particles, and the scaling of the moments with respect to the number of particles when the latter goes to infinity. Malyshev (2015) suggested to include in the model only the interactions between the closest neighbours to study the flow of charged particles. Notably, even the nearest-neighbours interactions case is proved to exhibit multiple phase transitions depending on the strength of the external force when the number of particles goes to infinity. Assuming zero external force, we show that interactions beyond the nearest ones lead to qualitatively new features of the system. In particular, we discover that the covariances between spacings exhibit the antiferromagnetic property, namely they periodically change sign depending on the parity of the number of spacings between them, while their amplitude decays. In the course of the proof of these results, a conditional Central Limit Theorem for dependent random variables is established which might have interest on its own (particularly due to negatively correlated variables). As a corollary conditional Central Limit Theorem is derived which confirms that the fluctuations in the considered ensemble are Gaussian.
The recording: YouTube
April 9, 16:45 msk
Stanislav Shaposhnikov, Lomonosov MSU, NRU HSE, Russia
Fokker-Planck-Kolmogorov equations and diffusion semigroups
The talk is devoted to the connections between Fokker-Planck-Kolmogorov equations and diffusion semigroups in the case when there exists a stationary probability solution. We will present the results about the solvability of Fokker-Planck-Kolmogorov equations and the existence of a Markovian semigroup with an invariant measure. Moreover we will give an answer to the old question about the uniqueness of the sub-Markovian semigroup generated by an elliptic operator in the space of functions integrable with respect to the stationary probability solution.
The recording: YouTube
April 2, 16:45 msk
Lomonosov readings
Elena Filichkina, Lomonosov MSU, Russia
On non-Markov processes satisfying the Kolmogorov-Chapman equations
The report considers examples of processes that satisfy the Kolmogorov-Chapman equations, but are not Markovian. In particular, the example proposed by Feller of a process with three or more states is analyzed in detail, and examples of processes with two states are considered, based on Bernstein's example of pairwise independent variables which are not mutually independent. It is shown that the Kolmogorov-Chapman equations do not uniquely determine a non-Markov process. And it is established that for non-degenerate Gaussian processes with a continuous covariance function, the satisfying of the Kolmogorov-Chapman equations is equivalent to the Markov property of the process.
Alexander Veretennikov, Lomonosov MSU, Russia
On new limit theorems and applications of limit theorems
A review of fresh results on LLN, CLT and some applications will be offered. The following results will be presented: theorems of strong, weak LLN, and LLN on a sublinear probability space; Dobrushin's type CLTs for non-homogeneous Markov chains; application of Bernoulli LLN to convergence of mixed derivatives of Bernstein type polynomials for functions of two variables, which is an analogue and expansion of a Kantorovich result for one-dimensional case.
The recording: YouTube
March 26, 16:45 msk
Bingyi Jing, Southern University of Science and Technology, China
Dynamic Data Selection in Large Model Training
The training of large models typically requires the use of internet-scale massive data. Data quality is crucial to model performance, making the selection of high-quality samples from such vast datasets a critical issue. To address this, we have redesigned the lifecycle of data during the training process from the ground zero, starting with the underlying training framework. However, numerous challenges arise in the large-scale application of dynamic data filtering within current large model training systems. This report explores how to tackle these challenges.
The recording: YouTube
March 19, 16:45 msk
Andrey Piatnitski, MIPT, Russia; UiT, Norway
On spectral properties of convolution operators with potential
The talk will focus on the spectral properties of the operator being the sum of a convolution operator and multiplication by a potential. Under the assumption that the potential is a real bounded function that tends to zero at infinity, and the convolution kernel is an even integrable function this operator is bounded and symmetric in L^2. We will describe both the essential and the discrete spectrum of this operator.
The recording: YouTube
March 12, 16:45 msk
Victor Kashtanov, NRU HSE, Tikhonov MIEM, Russia
On one new limit distribution
For a controlled semi-Markov process with catastrophes, which has a finite set of states, and the embedded Markov chain has several closed classes of recurrent states. A limit theorem (Rare Event Theorem) on the distribution of the moment of catastrophe is proved. Depending on the choice of the normalizing factor, the limit distribution has a jump at zero, a jump at infinity (an improper distribution), and in the region from zero to infinity is determined by a mixture (linear combination) of exponential distributions. There are normalizing factors when there are no jumps. A theorem on the structure of the first moment of distribution is proved. The mathematical expectation is a fractional-linear functional with respect to probability distributions that determine the Markov homogeneous randomized control strategy of the studied semi-Markov process.
The recording: YouTube
March 5, 16:45 msk
Yuri Yakubovich, St. Petersburg University, Russia
Different cluster orderings in Gibbs random samples
We consider samples from random discrete distributions and the corresponding exchangeable random partitions of countable sets. After recalling a general theory of exchangeable random partitions due to Kingman, we introduce a two-parametric Ewens family of exchangeable random partitions and its generalization, the so-called Gibbs model of random partitions. We are interested in various orders of clusters of exchangeable random partition of a countable set restricted to its finite subset. There are at least three natural orderings of blocks of random partitions: decreasing cluster sizes/frequencies, appearance order and value order, to be explained in detail during my talk. For the most studied one-parametric Ewens family it is known from works of Donnelly and co-authors that the appearance order and value order have the same distribution. I will explain that for a two-parametric generalization this is no longer the case, and describe an explicit procedure for passing from one order to another. This procedure works as well for the Gibbs frequencies in size-biased random order. The talk is based on joint work with Jim Pitman.
The recording: YouTube
February 26, 16:45 msk
Irina Shevtsova, Lomonosov MSU, Russia
Estimates of the rate of convergence to normal variance-mean mixtures
We consider a special class of one-dimensional scale-location mixtures of normal laws, where the mean is proportional to the variance. This class is very wide and includes generalized hyperbolic, generalized variance-gamma, Linnik, logistic, exponential-power, generalized Student (Lomax) laws and their skew modifications. We provide examples where such distributions appear as the limiting for special random sums and present estimates of the rate of weak convergence of mixed Poisson random sums to the corresponding limits. The estimates are based on the fundamental Berry-Esseen-type inequality for Poisson random sums from [Makarenko, Shevtsova // Mathematics, 2023], where the «constant» depends on the centering parameter (normalized expectation) of the random summands and, as this parameter goes to zero, decreases (up to 1.5 times as compared with the absolute constant) to the same value as if the summands were centered. This is crucial for variance-mean mixing since the corresponding centering parameter here is infinitesimal though may be nonzero. As a by-product, we compute the absolute moments of all orders of the Kolmogorov distribution.
The recording: YouTube
February 19, 16:45 msk
Andrei Lyulintsev, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Russia
Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable
A branching random walk on Z_{+} is considered, which corresponds to a Jacobi matrix. Previously, formulas for the average number of particles at an arbitrary fixed point in Z_{+} at time t > 0 were obtained in terms of the orthogonal polynomials associated with this matrix. In the present work, the application of the obtained results to certain models involving orthogonal polynomials of a discrete variable (Krawtchouk, Meixner and Poisson-Charlier polynomials) will be discussed.
The recording: YouTube
February 12, 16:45 msk
Dayue Chen, Peking University, China
A survey of the contact process
The contact process was introduced to describe the spread of a disease, is one of the earliest model of the interacting particle systems. It has been well studied and many profound properties have been discovered, while some basic problems remain to be open. For example, the exact value of the critical point is still unknown. In this talk I will first introduce the model, then review its properties and recent progress, with some inputs from my group.
The recording: YouTube
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