September 2018
Intermediate to advanced
288 pages
7h 38m
English
In a one-dimensional random walk, we study the motion of a point-like particle that is constrained to move along a straight line in one of only two directions (right and left). For each (random) movement, it can move one step to the right with a fixed probability p or to the left with a q probability. Each step is of equal length, and is independent of the others, as shown in the following diagram:

The position of the point after n steps—identified by its abscissa, X(n)—obviously contains a random term. We want to calculate the probability after n movements that the particle will return to the starting point (it ...
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