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The problem of determining the multiplicities of an eigenvalue of a product of companion matrices appears in the study of Random Walks in a Periodic Environment (RWPE), a type of
From the earlier studies of random walks on fractals it is known that the walk is ruled by two parameters, by the fractal dimension and an exponent describing the conductivity of
If a random walk characterized by conductances is started at the root of a tree, it is well known [3] that the escape probability equals the ratio of the effective conductance of
At the end of this note we show that (2) is not true in three dimensions, i.e., with probability one, the cut points of two independent three dimensional simple random walks
Our proof follows recent work by Denisov and Wachtel who used mar- tingale properties and a strong approximation of random walks by Brownian motion.. Therefore, we are able to
Generally, it seems to be difficult to obtain results for the finiteness of the expected values of the passage times when EX 2 = ∞ , not only for the reflected process, but for
We prove the moderate deviation principle for subgraph count statistics of Erd˝ os-Rényi random graphs.. This is equivalent in showing the moderate deviation principle for the trace
Roughly speaking, the Krawtchouk process is a system of non-colliding random walks in discrete time and the Charlier process is the continuous-time analogue (but note that they
