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The alloy model: Phase transitions and diagrams for a random energy model with mixtures
Markov Processes and Related Fields. 2019. Vol. 25. No. 4. P. 591-613.
Grabchak M., Molchanov S.
In press
In this paper we introduce the alloy model, which is a variant of Derrida’s random energy model (REM). The alloy model assumes that energy levels are independent and identically distributed (iid) random variables, whose distribution is a mixture of two distribution from the same location-scale family. These families are assumed to have either Weibull or Gumbel tails. Particular attention is paid to the case of normal distributions. For these we get more explicit results, which show that, for certain choices of the parameters, we can have two phase transitions, one first order and one second order.
Priority areas:
mathematics
Language:
English
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In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...
Added: March 31, 2017
Maslov V., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 3 P. 361-373
The notion of locally ideal liquid, similar to locally ideal fluid, is introduced. The distribution of locally ideal liquid is presented and compared with the one given by the van der Waals equation. The notion of phase transition from the metastable liquid state to the metastable solid state (glass) is introduced. © 2015, Pleiades Publishing, ...
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Molchanov S., Panov V., Russian Mathematical Surveys 2020 Vol. 75 No. 6 P. 1089-1132
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In this paper, the impact of lethal mutations on evolutionary dynamics of asexual populations is analyzed. We suggest distinguishing different definitions of lethality, which lead to different mathematical formalizations of the microscopic model. Most of the studies focus on polyphasic lethality, meaning that individuals carrying lethal mutations have no offspring but consume common resources. In ...
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Astrakharchik G., Kryuchkov P., Kurbakov I. et al., Crystals 2018 Vol. 8 No. 246 P. 1-26
Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and ...
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Nechaev S. K., Gorsky A., Avetisov V. A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 No. 96 P. 062309-1- 062309-14
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Grabchak M., Molchanov S., Theory of Probability and Its Applications 2019 Vol. 63 No. 4 P. 634-647
In this paper we study the asymptotic distributions, under appropriate normalization, of the sum $S_t = \sum_{i=1}^{N_t} e^{t X_i}$, the maximum $M_t = \max_{i\in\{1,2,\dots,N_t\}} e^{tX_i}$, and the $l_t$ norm $R_t=S_t^{1/t}$, when $N_t\to\infty$ as $t\to\infty$ and $X_1,X_2,\dots$ are independent and identically distributed random variables in the maximum domain of attraction of the reverse-Weibull distribution. ...
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In a recent paper we proposed a new model of the dynamics of
locally interacting particles (with a mean-field type interaction)
and proved that in the limit of weak interactions finite systems
of particles (or CML) may demonstrate both the synchronization,
and independent behavior (i.e. the phase transition takes place),
depending on fine properties of the interaction. Fundamental
technical limitation there ...
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Panov V., Statistics and Probability Letters 2017 Vol. 129 P. 379-386
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...
Added: July 10, 2017
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Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
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A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
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We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
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Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
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We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
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Представлен полиномиальный алгоритм корректировки расписания движения поездов для случая, когда один из путей двухпутной железной дороги становится недоступным, оставшийся путь содержит разъезд, а все поезда делятся на две категории: приоритетные поезда, например пассажирские, и обычные поезда, к которым относятся большинство грузовых поездов. Представленный алгоритм минимизирует негативное влияние, оказываемое блокировкой пути, сначала для приоритетных поездов, а ...
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Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
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Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
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Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
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