arXiv subjects

Igor Goncharenko

Publications and source records attributed to Igor Goncharenko.

4 recordsLinked to original sources

arXiv2010

Vicious Lévy flights

We study the statistics of encounters of Lévy flights by introducing the concept of vicious Lévy flights - distinct groups of walkers performing independent Lévy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time $t$ decays as $t^{-α}$ at late times. We compute $α$ up to the second order in $ε$-expansion, where $ε=σ-d$, $σ$ is the Lévy exponent and $d$ is the spatial dimension. For $d=σ$, we find the exponent of the logarithmic decay exactly. Theoretical values of the exponents are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2010

Vicious walks with long-range interactions

The asymptotic behaviour of the survival or reunion probability of vicious walks with short-range interactions is generally well studied. In many realistic processes, however, walks interact with a long ranged potential that decays in $d$ dimensions with distance $r$ as $r^{-d-σ}$. We employ methods of renormalized field theory to study the effect of such long range interactions. We calculate, for the first time, the exponents describing the decay of the survival probability for all values of parameters $σ$ and $d$ to first order in the double expansion in $ε=2-d$ and $δ=2-d-σ$. We show that there are several regions in the $σ-d$ plane corresponding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections for the first time.

cond-mat.stat-mech↗

arXiv2010

Perceiving the Social: A Multi-Agent System to Support Human Navigation in Foreign Communities

This paper describes a system developed to help people explore local communities by providing navigation services in social spaces created by the community members via communication and knowledge sharing. The proposed system utilizes data of a community's social network to reconstruct the social space, which is otherwise not physically perceptible but imaginary, experiential, yet learnable. The social space is modeled with an agent network, where each agent stands for a member of the community and has knowledge about expertise and personal characteristics of some other members. An agent can gather information, using its social "connections", to find community members most suitable to communicate to in a specific situation defined by the system's user. The system then deploys its multimodal interface, which "maps" the social space onto a representation of the relevant physical space, to locate the potential interlocutors and advise the user on an efficient communication strategy for the given community.

cs.CY↗

arXiv2009

Exact Spectral Dimension of the Random Surface

We propose a new method of the analytical computation of the spectral dimension which is based on the equivalence of the random walk and the q-state Potts model with non-zero magnetic field in the limit $q\to 0$. Calculating the critical exponent of the magnetization of this model on the dynamically triangulated random surface by means of a matrix model technique we obtain that the spectral dimension of this surface is equal to two.

hep-th↗