TY  - JOUR
A1  - Peng, Junhao
A1  - Sandev, Trifce
A1  - Kocarev, Ljupco
T1  - First encounters on Bethe lattices and Cayley trees
T2  - Communications in nonlinear science & numerical simulation
N2  - In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved.
KW  - Random walks
KW  - Survival probability
KW  - Mean first encounter time
KW  - Bethe
KW  - lattices
KW  - Cayley trees
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/63974
SN  - 1007-5704
SN  - 1878-7274
VL  - 95
PB  - Elsevier
CY  - Amsterdam
ER  -