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Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law
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 critical 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 answer 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.
Publication based on the results of:
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
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
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
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
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
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
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
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
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