Let b be an integer greater than 1 and let Wε=(Wn ε;n≥ 0) be a random walk on the b-ary rooted tree Ub, starting at the root, going up (resp. down) with probability 1/2 + ε (resp. 1/2 - ε), ε ∈ (0, ...

We study the behavior of random walk in random environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ...

A team from the Institute for Advanced Study, Emory University in the US, and the Weizmann Institute of Science, Israel, has developed a new mathematical framework to understand how humans store ...

STATEN ISLAND, N.Y. -- Have you ever noticed an abnormal growth on the trunk of a tree that looked rather tumorous -- all bumpy and wart-like? Examples can be seen on random trees just about anywhere.

Understanding the function of stochasticity in biological systems has been a long-standing challenge 1,2,3. Two main principles have been recognized. First, stochastic algorithms allow simpler genetic ...