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## Intermittency for branching walks with heavy tails

In press

Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the particles inside of the front are distributed very non-uniformly. The particles exhibit intermittent behavior in a large part of the region behind the front (i.e. the particles are concentrated only in very sparse spots there). The zone of non-intermittency (were particles are distributed relatively uniformly) extends with a power rate. This rate is found.

Silin V. P., Budaev V. P., Savin S. P. et al., Bulletin of the Lebedev Physics Institute 2016 Vol. 43 No. 4 P. 132-137

It is proposed to consider the scalings of anomalous transport (superdiusion), determined experimentally in turbulent plasma of the Earth's magnetosphere and laboratory plasma of thermonuclear facilities and processed using modern statistical cascade models of strong turbulence with intermittency, also within the approach of physical kinetics to the theory of plasma turbulence. ...

Added: February 26, 2017

Kolokolov I., Gamba A., Journal of Statistical Physics 1999 Vol. 94 No. 5/6 P. 759-777

We compute analytically the probability distribution function PP(ε) of the dissipation field ε=(∇θ)2 of a passive scalar θ advected by a d-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor–Kraichnan regime). The tail of the distribution is a stretched exponential: for ε→∞, ln PP(ε)∼−(d2ε)1/3. ...

Added: March 5, 2017

Kolokolov I., JETP Letters 2000 Vol. 71 No. 1 P. 12-14

Leading terms of the asymptotic behavior of the pair and higher order correlation functions for finite times and large distances have been calculated for the Burgers equation involving thermal noise. It is shown that an intermittence phenomenon occurs, whereby certain correlation functions are much greater than their reducible parts. ...

Added: March 5, 2017

Blank M., Доклады Академии наук 2013 Т. 448 № 6 С. 629-632

We give conditions for unique ergodicity for a discrete time collective
random walk on a continuous circle. Individual particles in this collective
motion perform independent (and different) random walks conditioned
by the assumption that the particles cannot overrun each other.
Deterministic version of this system is studied as well. ...

Added: November 25, 2014

Khabarova O., Timothy Sagitov, Kislov R. et al., JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2021 Vol. 126 No. 8 P. 1-25

We propose a new method of the automated identification of current sheets (CSs) that represents a formalization of the visual inspection approach employed in case studies. CSs are often identified by eye via the analysis of characteristic changes in the interplanetary magnetic field (IMF) and plasma parameters. Known visual and semi-automated empirical methods of CS ...

Added: September 10, 2021

Kolokolov I., Turitsyn K., Journal of Experimental and Theoretical Physics 2002 Vol. 94 No. 6 P. 1193-1200

For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics
of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This
means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...

Added: February 25, 2017

Chernousova E., Molchanov S., Mathematical Population Studies 2019 Vol. 26 No. 1 P. 47-63

For the critical branching random walk on the lattice ZdZd, 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 ...

Added: November 15, 2019

Tamm M., Majumdar S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 P. 021135

We compute analytically the mean number of common sites, WN(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N−d) plane, there are three distinct regimes for the asymptotic large-t growth of WN(t). These three regimes are separated by two critical lines d=2 and d=dc(N)=2N/(N−1) in the (N-d) plane. For d<2, WN(t)∼td/2 for large t (the N dependence is ...

Added: November 18, 2013

Kolokolov I., Chertkov M., Falkovich G., Physical Review Letters 1998 Vol. 80 No. 10 P. 2121-2124

The probability density function (PDF) of passive scalar dissipation P sed is found analytically in
the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The
tail of PDF is shown to be stretched exponent. ...

Added: March 5, 2017

Decrouez G. G., Borovkov K., Theory Probability and its Applications 2012 Vol. 57 No. 3 P. 396-418

We consider a transformed Ornstein--Uhlenbeck process model that can be a good candidate for modeling real-life processes characterized by a combination of time-reverting behavior with heavy distribution tails. We begin with presenting the results of an exploratory statistical analysis of the log prices of a major Australian public company, demonstrating several key features typical of ...

Added: September 29, 2014

Kazaryan M., Uribe-Vargas R., Moscow Mathematical Journal 2020 Vol. 20 No. 3 P. 511-530

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. ...

Added: August 24, 2020

Alexander Gushchin, Pavlyukevich I., Ritsch M., Statistical Inference for Stochastic Processes 2020 Vol. 23 No. 3 P. 553-570

We consider the problem of estimation of the drift parameter of an ergodic Ornstein–
Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed
continuously on a long time interval [0, T ], T →∞. We prove that the statistical model is
locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically
efficient. ...

Added: October 27, 2020

Veretennikov A., Zverkina G., , in : Distributed Computer and Communication Networks. 18th International Conference, DCCN 2015, Moscow, Russia, October 19-22, 2015, Revised Selected Papers. Vol. 601.: Switzerland : Springer, 2016. P. 358-369.

A computable estimate of the readiness coefficient for a standard binary-state system is established in the case where both working and repair time distributions possess heavy tails. ...

Added: May 11, 2016

Burov A. A., Shalimova E. S., Mechanics of Solids 2016 Vol. 51 No. 4 P. 395-405

The motion of a heavy bead on the surface of a parabolic bowl rotating at a constant angular velocity about its axis, which coincides with the vertical, is considered. It is assumed that the dry friction force acts between the bead and the bowl. The sets of nonisolated relative equilibria of the bead on the ...

Added: November 7, 2016

Kolokolov I., Lebedev V., Falkovich G. et al., International Journal of Modern Physics B 1997 Vol. 11 No. 26/27 P. 3223-3245

We consider
the tails of probability density functions (PDF) for different characteristics
of velocity that satisfies Burgers equation driven by a large-scale force.
The saddle-point approximation is employed in the path integral
so that the calculation of the PDF tails
boils down to finding the special field-force configuration (instanton) that
realizes the extremum of probability. We calculate high moments of the ...

Added: March 6, 2017

Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review Letters 1997 Vol. 78 No. 8 P. 1452-1455

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For ...

Added: March 6, 2017

Mikhailov E. A., Elistratov S. A., Grachev D., Computational Mathematics and Modeling 2021 Vol. 32 No. 1 P. 45-51

We investigate a stochastic model of the galactic dynamo in the planar approximation, assuming that turbulent diffusivity is a renewal process. For linear and nonlinear modifications of this model, numerical methods are applied to construct statistical moments and correlation tensors of the magnetic field. ...

Added: October 31, 2021

Manita O. A., Veretennikov A., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 89-106

Rate of convergence is studied for a diffusion process on the half line with a non-sticky reflection to a heavy-tailed 1D invariant distribution which density on the half line has a polynomial decay at infinity. Starting from a standard receipt which guarantees some polynomial convergence, it is shown how to construct a new non-degenerate diffusion ...

Added: November 15, 2018

Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph

Vsevolod Chernyshev, Tolchennikov A. A., Electronic Notes in Discrete Mathematics 2018 Vol. 70 P. 31-35

The asymptotics of the number of possible endpoints of a random walk on a metric
graph with incommensurable edge lengths is found. ...

Added: December 10, 2018

Davydov Y., Konakov V., , in : Modern problems of stochastic analysis and statistics - Selected contributions in honor of Valentin Konakov. : Heidelberg : Springer, 2017. P. 3-24.

In the first part of the paper we consider a "random flight" process in \(R^d\) and obtain the weak limits under different transformations of the Poissonian switching times. In the second part we construct diffusion approximations for this process and investigate their accuracy. To prove the weak convergence result we use the approach of ...

Added: December 9, 2017

Davydov Y., Konakov V., Random walks in non homogeneous Poissonian environment / Cornell University. Series math "arxiv.org". 2016. No. 1609.07066.

We consider the moving particle process in Rd which is defined in the following way. There are two independent sequences (Tk) and (dk) of random variables. The variables Tk are non negative and form an increasing sequence, while variables dk form an i.i.d sequence with common distribution concentrated on the unit sphere. The values dk ...

Added: September 23, 2016

Valba O. V., Nechaev S., Tamm M., Химическая физика 2012 Т. 31 С. 23

В работе определяется свободная энергия связывания двух молекул РНК и обсуждаются такие ста тистические свойства, как флуктуации средней энергии связывания двух молекул РНК и распреде ление длин петель в образованной структуре. Анализ зависимости удельной свободной энергии комплекса двух длинных случайных молекул РНК от числа с типов нуклеотидов позволил выдви нуть гипотезу о выделенной роли используемого ...

Added: November 19, 2013

Боровков А. А., Cambridge University Press, 2020

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established ...

Added: March 30, 2021

Kolokolov I., Falkovich G., Chertkov M. et al., Physical Review Letters 1999 Vol. 83 No. 20 P. 4065-4068

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity permits a systematic analysis of the Lagrangian path dynamics. We find analytically the moments and multipoint correlation functions of the magnetic field at small ...

Added: March 5, 2017