科研之友
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摘要
We study the starvation of a lattice random walker in which each site initially contains one food unit and the walker can travel S steps without food before starving. When the walker encounters food, it is completely eaten, and the walker can again travel S steps without food before starving. When the walker hits an empty site, the time until the walker starves decreases by 1. In spatial dimension d = 1, the average lifetime of the walker <tau > proportional to S, while for d > 2, <tau > similar or equal to exp(S-omega), with omega -> 1 as d -> infinity; the latter behavior suggests that the upper critical dimension is infinite. In the marginal case of d = 2, <tau > proportional to S-z, with z approximate to 2. Long-lived walks explore a highly ramified region so they always remain close to sources of food and the distribution of distinct sites visited does not obey single-parameter scaling.
- 出版日期2014-12-1
