In book
* 3: Combinatorics. , Providence: AMS, 2023.
Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set.
For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...
Added: May 28, 2026
Ермолаев Е. С., Applied Network Science 2025 Vol. 10 Article 30
Recent advances in complex systems have highlighted the utility of simplicial complexes for modeling higher-order interactions, particularly in biological and physical networks. This study presents enhanced Simplex2Vec, an adaptation of the Simplex2Vec algorithm, to facilitate community detection within such structures. We compare enhanced Simplex2Vec’s efficacy against the Leiden algorithm and Spectral clustering using 7 distinct ...
Added: December 30, 2025
Заславский А. А., Skopenkov M., Ustinov A., В кн.: Элементы математики в задачах: через олимпиады и кружки—к профессии.: М.: МЦНМО, 2018.
The chapter is devoted to random walks and electrical networks. ...
Added: October 13, 2025
Баранов Д. В., Skopenkov M., Ustinov A., Математическое просвещение 2011 № 15 С. 229–230
This collection of problems is based on the project “Random walks and electric circuits” of the XXII Summer Conference of the Tournament of Cities and problem 14.12 from the problem book “Mathematical Enlightenment” (issue 14, p. 274). ...
Added: October 9, 2025
Skopenkov M., Смыкалов В., Ustinov A., Математическое просвещение 2012 № 16 С. 25–47
The article is devoted to the mathematical theory of electrical networks. ...
Added: October 9, 2025
Ustinov A., Skopenkov M., Пахарев А. А., Математическое просвещение 2014 № 18 С. 33–65
The article presents the mathematical theory of electrical networks. ...
Added: October 9, 2025
Danilov V., Михайлова С. О., Математические заметки 2024 Т. 116 № 6 С. 881–897
В этой статье на примере случайных блужданий будет представлен метод решения параболических задач на сетке. Ввиду стохастических свойств случайных блужданий ранее полученные интерполяционные методы решения гиперболических задач (преобразование Фурье, теорема В. А. Котельникова) на сетках неприменимы. В данной статье строится формальная асимптотика фундаментального решения задачи Коши и краевых задач для параболического случайного блуждания по решетке, ...
Added: November 26, 2024
V. Gorbounov, Guterman L., Bychkov B. et al., Journal of Geometry and Physics 2025 Vol. 207 P. 0
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the disc obtained in \cite{L}, \cite{CGS} and \cite{BGKT}. In particular, we state an explicit connection between these works ...
Added: October 4, 2024
Konakov V., Menozzi S., / Series arXiv "math". 2023. No. 2312.06222.
Abstract. We prove central and local limit theorems for random walks on the Poincar´e hyperbolic space of
dimension n ě 2. To this end we use the ball model and describe the walk therein through the M¨obius addition
and multiplication. This also allows to derive a corresponding law of large numbers. ...
Added: December 12, 2023
Molchanov S., Куценко В. А., Яровая Е. Б., Успехи математических наук 2023 Т. 78 № 5(473) С. 181–182
Условия надкритичности для ветвящихся блужданий в случайной убивающей среде с единственным центром размножения. ...
Added: November 3, 2023
B. Bychkov, V. Gorbounov, Talalaev D. et al., Moscow Mathematical Journal 2023 Vol. 23 No. 2 P. 133–167
We refine the result of T. Lam on embedding the space En of electrical networks on a planar graph with n boundary points into the totally non-negative Grassmannian Gr≥0(n−1,2n) by proving first that the image lands in Gr(n−1,V)⊂Gr(n−1,2n), where V⊂R2n is a certain subspace of dimension 2n−2. The role of this reduction of the dimension of the ambient space is crucial for us. We show ...
Added: June 12, 2023
Galkin S., Belmans P., Mukhopadhyay S., / Series math "arxiv.org". 2020. No. 2009.05568.
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of ...
Added: April 15, 2021
Боровков А. А., Cambridge University Press, 2020.
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established ...
Added: March 30, 2021
Загвоздина К. О., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: М.: МИЭМ НИУ ВШЭ, 2019. С. 46–47.
Данное исследование посвящено задаче определения
влияния двух решётчатых моделей конформационного
пространства и пространства последовательностей белковых макромолекул (модели Изинга и HP-модели) на геометрические свойства случайных блужданий без самопересечений. Анализ проведён на основе средних квадратов
радиуса и радиуса инерции. Максимальная длина последовательности равна 10. ...
Added: October 31, 2019
Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph
Vsevolod Chernyshev, Tolchennikov A. A., Electronic Notes in Discrete Mathematics 2018 Vol. 70 P. 31–35
The asymptotics of the number of possible endpoints of a random walk on a metric
graph with incommensurable edge lengths is found. ...
Added: December 10, 2018
Davydov Y., Konakov V., , in: Modern problems of stochastic analysis and statistics - Selected contributions in honor of Valentin Konakov.: Heidelberg: Springer, 2017. P. 3–24.
In the first part of the paper we consider a "random flight" process in \(R^d\) and obtain the weak limits under different transformations of the Poissonian switching times. In the second part we construct diffusion approximations for this process and investigate their accuracy. To prove the weak convergence result we use the approach of ...
Added: December 9, 2017