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Title: Comparing numerical results for branching random walks in non random and random media Authors:  Vladimir Kutsenko - Lomonosov Moscow State University (Russia) [presenting]
Elena Yarovaya - Lomonosov Moscow State University (Russia)
Abstract: Continuous-time branching random walks (BRWs) on a multidimensional lattice in a random branching medium are considered. The branching medium may contain a finite or non-finite number of particle generation sources. The underlying walk of particles is symmetric, homogeneous by space, and irreducible with a finite variance of jumps. The vast majority of the results obtained in the theory of BRWs in random media are asymptotic. In such BRWs, at large times, rare fluctuations of the medium may lead to anomalous properties of a particle field such as ``intermittency''. At the same time, the study of BRWs at finite time intervals seems to be a difficult task that has not yet been solved satisfactorily enough. Thus, the main goal of the simulation is to investigate whether it is possible to obtain qualitative and quantitative results predicted by the theory already at finite times. A similar task for BRWs in non-random media has been previously considered. However, to the best of our knowledge, there are no similar studies related to the simulation of BRWs in random branching media. Here, the phenomenon of intermittency is of the most significant interest and importance. Based on the simulation results, we managed to show that intermittency can be observed in random media even over finite time intervals.