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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
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Some references to understand the proof of a theorem about simple random walk on galton wats...
Mathematicians Lyons,Pemantle and Peres have proved in the paper entitled "Ergodic Theory on Galton-Watson Trees: Speed of Random Walk and Dimension of Harmonic Measure" that the speed of a simple random …
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How to get some information about a random variable if we know very little about its distrib...
Suppose that $X, Y$ are random variables,both from a probability space to $(0,\infty]$, such that X and $1+Y$ have the same distribution, $Y=Z_1$ with probability equals half, otherwise $Y= \frac{Z_1 …