Cookie branching random walks

作者：Bartsch Christian^*; Kochler Michael; Kochler Thomas; Mueller Sebastian; Popov Serguei

来源：Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2013, 10(1): 323-358.

• Recurrence
• Transience
• Self-Interacting Branching Process

We consider branching random walks in discrete time where at each time unit particles first produce offspring and thereafter the produced offspring particles move independently according to some nearest neighbour random walk. In our model, the branching random walks live on Z, and the particles behave differently in visited and unvisited sites. Informally, each site on the positive half-line contains initially a cookie. On the first visit of a site its cookie is removed and particles at positions with a cookie reproduce and move differently from particles on sites without cookies. Therefore, the movement and the reproduction of the particles depend on the previous behaviour of the population of particles. %26lt;br%26gt;We give a classification in recurrence and transience, i.e. whether infinitely many particles visit the origin or not.

• 出版日期2013