Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Multidimensional catalytic branching random walk with regularly varying tails. / Bulinskaya, Ekaterina Vl.
ICoMS 2019 - Proceedings of 2019 2nd International Conference on Mathematics and Statistics. Association for Computing Machinery, 2019. p. 6-13 (ACM International Conference Proceeding Series).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - Multidimensional catalytic branching random walk with regularly varying tails
AU - Bulinskaya, Ekaterina Vl
N1 - Publisher Copyright: © 2019 Association for Computing Machinery.
PY - 2019/7/8
Y1 - 2019/7/8
N2 - Catalytic branching random walk (CBRW) describes reproduction of particles and their movement in space. The particles may give offspring in the presence of catalysts. Consider CBRW model where the particles perform a random walk over a multidimensional lattice, without procreation outside the catalysts. The latter take a finite number of fixed positions at the lattice. We study the particles spread in case of non-extinction of population initiated by a single particle. The rate of population spread depends essentially on the distribution tails of the random walk jumps. Consider the jumps with independent (or close to independent) components having regularly varying “heavy’’ tails. The main results show that, after a proper normalization of positions, in the time limit the particles concentrate on a random set, located at the coordinate axes. For a two-dimensional case, the limiting set forms a cross, and, for any higher dimension d, it is a collection of d segments containing the origin. The joint distribution of such segments lengths is found and the time-limit is understood in the sense of weak convergence. This radically differs from the known results for both the CBRW with “light” and semi-exponential distribution tails of the random walk jumps.
AB - Catalytic branching random walk (CBRW) describes reproduction of particles and their movement in space. The particles may give offspring in the presence of catalysts. Consider CBRW model where the particles perform a random walk over a multidimensional lattice, without procreation outside the catalysts. The latter take a finite number of fixed positions at the lattice. We study the particles spread in case of non-extinction of population initiated by a single particle. The rate of population spread depends essentially on the distribution tails of the random walk jumps. Consider the jumps with independent (or close to independent) components having regularly varying “heavy’’ tails. The main results show that, after a proper normalization of positions, in the time limit the particles concentrate on a random set, located at the coordinate axes. For a two-dimensional case, the limiting set forms a cross, and, for any higher dimension d, it is a collection of d segments containing the origin. The joint distribution of such segments lengths is found and the time-limit is understood in the sense of weak convergence. This radically differs from the known results for both the CBRW with “light” and semi-exponential distribution tails of the random walk jumps.
KW - Catalytic branching random walk
KW - Heavy tails
KW - Population front
KW - Regularly varying tails
KW - Spread of population
KW - Supercritical regime
UR - http://www.scopus.com/inward/record.url?scp=85072808965&partnerID=8YFLogxK
U2 - 10.1145/3343485.3343493
DO - 10.1145/3343485.3343493
M3 - Conference contribution
AN - SCOPUS:85072808965
T3 - ACM International Conference Proceeding Series
SP - 6
EP - 13
BT - ICoMS 2019 - Proceedings of 2019 2nd International Conference on Mathematics and Statistics
PB - Association for Computing Machinery
T2 - 2nd International Conference on Mathematics and Statistics, ICoMS 2019
Y2 - 8 July 2019 through 10 July 2019
ER -
ID: 21792855