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Stanislav Molchanov
University of North Carolina at Charlotte
CombinatoricsRandom walkPhysicsMathematical analysisMathematics
200Publications
28H-index
3,188Citations
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Publications 185
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#1Molchanov Stanislav (HSE: National Research University – Higher School of Economics)
#2Panov Vladimir (HSE: National Research University – Higher School of Economics)H-Index: 1
ABSTRACTIn this paper, we consider limit laws for the model, which is a generalization of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, while the second has the mean na with some a∈R, and the variance σ≠1. The phase space (a,σ)⊂R×R+ is divided into several domains, where after appropriate normalization, th...
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#1Elena Chernousova (MIPT: Moscow Institute of Physics and Technology)H-Index: 2
#2Ostap Hryniv (Durham University)H-Index: 7
Last. Stanislav Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 28
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ABSTRACTIn a population model in continuous space, individuals evolve independently as branching random walks subject to immigration. If the underlying branching mechanism is subcritical, the model...
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#1Stanislav Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 28
#2Boris Vainberg (UNCC: University of North Carolina at Charlotte)H-Index: 16
Symmetric random walks in R^dand Z^dare considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all xand t asymptotic behavior at infinity of the transition probability (fundamental solution of the corresponding parabolic convolution operator) is found. Front propagation of ecological waves in the corresponding population dynamics models is described.
1 CitationsSource
#1Michael Cranston (UCI: University of California, Irvine)H-Index: 18
#2Stanislav Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 28
We begin with the reference measure P0 induced by simple, symmetric nearest neighbor continuous time random walk on Zd starting at 0 with jump rate 2d and then define, for β ⩾ 0, t > 0, the Gibbs probability measure Pβ,t by specifying its density with respect to P0 as \({{d{P_{\beta, t}}} \over {d{P^0}}} = {Z_{\beta, t}}{(0)^{-1}}{{\rm{e}}^{\beta \int_0^t {{\delta _0}({x_s})ds}}},\) (0.1) where \({Z_{\beta, t}}(0) \equiv {E^0}{\rm{[}}{{\rm{e}}^{\beta \;\int_0^t {{\delta _0}({x_s})ds}}}].\). This...
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#1Yaqin FengH-Index: 1
#2Stanislav MolchanovH-Index: 28
Last. Elena YarovayaH-Index: 9
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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.
We consider a continuous-time symmetric branching random walk on the ddimensional lattice, d\ge 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...
#1Elena Chernousova (MIPT: Moscow Institute of Physics and Technology)H-Index: 2
#2Stanislav Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 28
For the critical branching random walk on the lattice ${{\mathbb Z}^d}Zd, in the case of an arbitrary total number of produced offspring spreading on the lattice from the parental particle, the existence of a limit distribution (which corresponds to a steady state (or statistical equilibrium)) of the population is proved. If the second factorial moment of the total number of offspring is much larger than the square of the first factorial moment, then the limit particle field displays strong d...
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#2Stéphane MenozziH-Index: 11
Last. Stanislav MolchanovH-Index: 28
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#1Gregory DerfelH-Index: 9
#2Yaqin FengH-Index: 1
Last. Stanislav MolchanovH-Index: 28
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1 CitationsSource
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