• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
Researchers from HSE MIEM and Samara University have developed the LRF-3D algorithm to automatically bypass idle nodes in three-dimensional networks-on-chip. Thanks to its hierarchical architecture, the algorithm outperforms existing solutions in both speed and path accuracy, improving processor reliability for use in data centres, supercomputers, and AI computing. The source code and test results are publicly available.
August 24, 2026
Researchers Develop Method for Direct Generation of Regulatory DNA
Researchers at HSE University have developed a model for generating promoters and enhancers—DNA sequences that regulate gene activity. The model works directly with DNA nucleotides, without first transforming them into a continuous numerical representation. This solution could be useful for applications in synthetic biology and gene therapy. The study results were presented at the ICLR 2026 Workshop ‘Generative AI in Genomics (Gen^2): Barriers and Frontiers.’
August 21, 2026
Social Integration: At the Crossroads of Knowledge and Values
The International Laboratory for Social Integration Research (ILSIR) at HSE University studies the challenges faced by vulnerable groups and explores ways to help them participate fully in everyday life. To develop effective solutions, the laboratory’s researchers combine cutting-edge methods with practical fieldwork. In this interview with the HSE News Service, Laboratory Head Elena Iarskaia-Smirnova discusses the laboratory’s work.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law

Methodology and Computing in Applied Probability. 2021. Vol. 23. No. 3. P. 85–102.
Balashova D., Molchanov S., Yarovaya E.

We consider a continuous-time symmetric branching random walk on the d-dimensional lattice, d ≥ 1, and assume that at the initial moment there is one particle at every lattice point. Moreover, we assume that the underlying random walk has a finite variance of jumps and the reproduction law is described by a continuous-time Markov branching process (a continuous-time analog of a Bienamye-Galton-Watson process) at every lattice point. We study the structure of the particle subpopulation generated by the initial particle situated at a lattice point x. We replay why vanishing of the majority of subpopulations does not affect the convergence to the steady state and leads to clusterization for lattice dimensions d = 1 and d = 2.

Research target: Mathematics
Language: English
DOI
Keywords: critical branching process limit theorems population dynamicsBranching random walk
Publication based on the results of:
Phase transitions and bifurcations in mathematical models of biophysics, quantum mechanics, disordered systems, magnetohydrodynamics, population dynamics, limit theorems of probability theory (2021)
Similar publications
Orbifold Saito theory of A and D type singularities
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Non-axiomatizability of modal predicate logics of Dedekind-complete linear orders with constant domains
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Semi-Interlaced Polytopes
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems. Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
A new spin on polynomial relations among kappa classes
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Any Topological Recursion on a Rational Spectral Curveis KP Integrable
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Сплетенный мир: кошка перевернулась. Доклад Римскому клубу
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Multiplicity-free products of Schubert divisors
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Mukai models of Fano varieties
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Mukai bundles on Fano threefolds
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Full exceptional collections on the symplectic isotropic Grassmannians
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Analog of theta-lifting for a curve over dual numbers over a finite field
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Quasi-periodic structures and "shrimps" in chaos on the example a two-mode van der Pol generator
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results.
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Schools and Hospitals Close to Home: Impact of Social Infrastructure on Population Dynamics
M. O. Balaban, Vasilizhenko A. A., L. B. Karachurina et al., Regional Research of Russia 2026 Vol. 16 No. 1 P. 151–169
The population dynamics of settlements are determined by many different factors, including, as research shows, the availability of educational and healthcare facilities (i.e., basic social infrastructure) close to home. One can assume a two-way relationship: a decrease in population entails a reduction in the number of assigned students in schools and healthcare institutions and, as a result, the ...
Added: May 23, 2026
Школы и больницы рядом с домом: влияние социальной инфраструктуры на динамику численности населения
Balaban M., Василиженко А. А., Karachurina L. B. et al., Известия РАН. Серия географическая 2026 Т. 90 № S1 С. 208–230
The dynamics of population size in settlements are determined by a wide range of factors, among which, as research shows, is the availability of educational and healthcare institutions (i.e., basic social infrastructure) within close proximity to homes of residents. A bidirectional relationship can be assumed: a decline in population size leads to a reduction of ...
Added: November 7, 2025
Базовая социальная инфраструктура в населенных пунктах России и динамика численности их населения
Karachurina L. B., Mkrtchyan N. V., Социологические исследования 2025 № 5 С. 109–124
Receiving education and healthcare services is a basic need of the population, therefore, providing the population with access to social infrastructure institutions (various types of schools, preschool institutions, hospitals, rural outpatient clinics) is an important task of regional and municipal authorities. If by “access” we mean “the availability of social infrastructure at the place of ...
Added: July 5, 2025
Особенности Москвы как мирового цифрового мегаполиса
Arkhipova M., Sirotin V., В кн.: Цифровая экономика как драйвер экономического и социального развития: материалы IV международной научной конференции.: М.: МГИМО (У) МИД РФ, 2023. Гл. 3 С. 39–56.
Цифровая трансформация, охватывающая многие сферы социальноэкономической жизни общества, является одним из наиболее актуальных и перспективных трендов в развитых странах и, в особенности, в крупных мегаполисах. В России, как и в большинстве стран мира, столица берет на себя ведущую роль в сфере внедрения инноваций и апробации передовых технологий как в области управления и организации социального ландшафта, ...
Added: January 12, 2024
Цифровая экономика как драйвер экономического и социального развития: материалы IV международной научной конференции
М.: МГИМО (У) МИД РФ, 2023.
В сборнике статей представлены результаты исследований по проблемам экономического роста и развития экономики, использования больших данных и информационнокоммуникационных технологий в бизнес-среде и на государственном уровне. Авторами предлагаются научно обоснованные теоретические, методологические и практические подходы, предназначенные для решения актуальных вопросов развития экономики и ё финансов в современных условиях, исследуется генезис проблем современной экономической науки и тенденции ...
Added: January 12, 2024
Limit theorems for random walks in the hyperbolic space
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
Моделирование миграционных и демографических процессов с использованием FLAME GPU
Makarov V., Bakhtizin A., Beklaryan G. et al., Бизнес-информатика 2022 Т. 16 № 1 С. 7–21
This article presents an approach to modeling migration and demographic processes using a framework designed for large-scale agent-based modeling – FLAME GPU. This approach is based on the previously developed simulation model of interaction between two communities: migrants and natives that is implemented in the AnyLogic simulation software. The model has had a low dimensionality ...
Added: May 31, 2022
Spatiotemporal dynamics of pine marten (Martes martes), mountain hare (Lepus timidus), and red squirrel (Sciurus vulgaris) trail activity in the European southern taiga
Zheltukhin A. S., Puzachenko Y. G., Kotlov I. et al., Biology Bulletin Reviews 2017 Vol. 7 No. 1 P. 37–55
Observations of trail activity of the martens, mountain hares, and red squirrels in winter along fixed routes in the Central Forest Reserve showed its high variability and synchronism in time and space. Polynomial dependence of the trail activity and correlation between spatial distribution of marten, mountain hare and squirrel are detected. The influence of weather ...
Added: March 27, 2022
Stability and Instability of Steady States for a Branching Random Walk
Feng Y., Molchanov S., Yarovaya E., Methodology and Computing in Applied Probability 2021 Vol. 23 P. 207–218
We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a steady state. ...
Added: October 31, 2021
Steady state of lattice population with immigration
Chernousova E., Feng Y., Hryniv O. et al., Mathematical Population Studies 2021 Vol. 28 No. 2 P. 63–80
In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An ...
Added: October 31, 2021
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit