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Limit shape for the dimer model
Кучумов Н. И.
We prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states.
Sergei L. Semakov, Cambridge Scholars Publishing, 2024.
The behavior of any real system is a process to a greater or lesser degree probabilistic. As a rule, it is impossible to specify exactly which external influences and internal mechanisms of interaction of the system components will be decisive in the future. As a consequence, we cannot accurately predict the behavior of the system. ...
Added: March 18, 2026
Semakov S., Semakov I., IEEE Transactions on Aerospace and Electronic Systems 2022 Vol. 58 No. 6 P. 5425–5442
We propose the method for calculating the probability of a safe landing for ship-based aircraft. We define a safe landing as the event that the initial touch of the landing surface by an aircraft occurs on a given segment of the deck, and at the time of this contact, the phase coordinates of the aircraft ...
Added: August 9, 2025
Sergei L. Semakov, , in: 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT) (Malta, Valletta, July 01–04, 2024).: IEEE, 2024. P. 697–699.
A technology is proposed for estimating the probability that the share price will leave the established corridor by a given point in time. The exact expression is obtained for the required probability under the assumption that the behavior of the share price is described by the well-known model of Samuelson, according to which the relative ...
Added: August 4, 2025
М.: Математический институт им. В. А. Стеклова РАН, 2024.
This volume is dedicated to the 80th birthday of Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences. The volume includes articles on topology, geometry, combinatorics, and mathematical physics, the areas in which V. M. Buchstaber is a recognized world leader and the head of an active scientific school. Most of the articles are written ...
Added: January 15, 2025
Singapore: Springer, 2024.
This book gathers contributions on a variety of flowing collective systems. While primarily focusing on pedestrian dynamics, it also reflects the latest developments in areas such as vehicular traffic and granular flows and addresses related emerging topics such as self-propelled particles, data transport, swarm behaviour, intercellular transport, and individual interactions to complex systems. Combining fundamental ...
Added: October 4, 2024
Budkov Y., Брандышев П. Е., Journal of Chemical Physics 2023 Vol. 159 No. 17 Article 174103
Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an ...
Added: November 2, 2023
Springer, 2022.
This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022.
The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on computational methods ...
Added: December 26, 2022
Dyachenko A., Studies in Applied Mathematics 2020 Vol. 144 No. 4 P. 493–503
One of the essential tasks of the theory of water waves is a construction of simplified mathematical models, which are applied to the description of complex events, such as wave breaking, appearing of freak waves in the assumption of weak nonlinearity. The Zakharov equation and its simplification, such as nonlinear Schrodinger equations and Dysthe equations, ...
Added: October 21, 2022
Кучумов Н. И., / Series arXiv "math". 2021.
We study random domino tilings of a multiply-connected domain with a height function defined on the universal covering space of the domain. We prove a large deviation principle for the height function in two asymptotic regimes. The first regime covers all domino tilings of the domain. We also prove a law of large numbers for ...
Added: June 24, 2022
Cham: Birkhäuser, 2020.
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, ...
Added: November 3, 2021
M.: RUDN, 2020.
The materials of the 5th International conference on stochastic methods are presented including the following directions: probability and statistics (analytic modelling, asymptotic methods and limit theorems, stochastic analysis, Markov processes and martingales, actuarial and financial mathematics, et al.); applications of stochastic methods (queueing theory and stochastic networks, reliability theory and risk analysis, probability in indistry, ...
Added: January 27, 2021
Makarov A. A., Yaschenko I., Высоцкий И. Р. et al., М.: Просвещение, 2020.
Учебное пособие предназначено для знакомства учащихся с формами представления и описания данных в статистике, случайными событиями, вероятностью и ее свойствами. В пособии в равной мере уделено внимание статистике, комбинаторике и теории вероятностей и их роли в изучении явлений окружающего мира. ...
Added: October 28, 2020
Mazzucchi S., Moretti V., Remizov I. et al., / Series arXiv "math". 2020.
Feynman formulas are representations of solutions to initial value problems, for some parabolic and Schrödinger equations, by the limits of integrals over finite Cartesian powers of some spaces. Two versions of these formulas which were suggested by Feynman himself are associated with names of Trotter and Chernoff respectively. These formulas can be interpreted as approximations ...
Added: August 10, 2020
Budkov Y., Physical Chemistry Chemical Physics 2020 Vol. 22 P. 14756–14772
In this article, I summarize my theoretical developments in the statistical field theory of salt solutions of zwitterionic and multipolar molecules. Based on the Hubbard-Stratonovich integral transformation, I represent configuration integrals of dilute salt solutions of zwitterionic and multipolar molecules in the form of functional integrals over the space-dependent fluctuating electrostatic potential. In the mean-field ...
Added: June 11, 2020
Ivanov F., Rybin P., Afanassiev V. et al., , in: 2019 XVI International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY).: IEEE, 2019. P. 27–31.
Added: March 17, 2020
Switzerland: Springer, 2019.
This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Data Processing, IDP 2016, held in Barcelona, Spain, in October 2016.
The 11 revised full papers were carefully reviewed and selected from 52 submissions. The papers of this volume are organized in topical sections on machine learning theory with applications; intelligent data processing in life ...
Added: February 8, 2020
Burovskiy E., Janke W., Guskova M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 6 P. 063303-1–063303-8
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results ...
Added: November 5, 2019
S.M. Khoroshkin, M. G. Matushko, Journal of Mathematical Physics 2019 Vol. 60 No. 7 P. 071706-1–071706-22
We present a construction of an integrable model as a projective type limit of Calogero-Sutherland models of N fermionic particles, when N tends to infinity. Explicit formulas for limits of Dunkl operators and of commuting Hamiltonians by means of vertex operators are given. ...
Added: September 19, 2019
Shchur L., Barash L., Weigel M. et al., , in: Supercomputing. RuSCDays 2018. Communications in Computer and Information Science, vol 965. Springer, Cham.: Springer, 2019. P. 354–366.
Population annealing is a novel Monte Carlo algorithm designed for simulations of systems of statistical mechanics with rugged free-energy landscapes. We discuss a realization of the algorithm for the use on a hybrid computing architecture combining CPUs and GPGPUs. The particular advantage of this approach is that it is fully scalable up to many thousands ...
Added: April 6, 2019
Fehér L., Marshall I., Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics 2019 P. 1217–1262
Integrable many-body systems of Ruijsenaars–Schneider–van Diejen type displaying action-angle duality are derived by Hamiltonian reduction of the Heisenberg double of the Poisson–Lie group SU(2n). New global models of the reduced phase space are described, revealing non-trivial features of the two systems in duality with one another. For example, after establishing that the symplectic vector space ...
Added: March 7, 2019