For a strongly subcritical branching process (Zn)n[greater-or-equal, slanted]0 in random environment the non-extinction probability at generation n decays at the same exponential rate as the expected generation size and given non-extinction at n the conditional distribution of Zn has a weak...

Let {[xi]n} be a subcritical branching process in random environment with independent identically distributed generating functions fn(s). It is shown that if there exists a positive number æ such that E(f0'(1))æ=1 then, for x-->+[infinity],where K is a positive constant.

We discuss recent findings suggesting that an inverse square probability density distribution P(ℓ)∼ℓ−2 of step lengths ℓ leads to an optimal random search strategy for organisms that can search efficiently for randomly located objects that can only be detected in the limited vicinity...