t*****e
发帖数: 53 | 1 can anybody help to use a simple probability theory to explain. no
stochastic calculus please!
there is pentagon with five bugs sitting in the middle point of each edge.
Each bug can go both directions along the edge. and they can change
direction any time. whats the probability that 2 or 3 bugs can meet each
other. | t*******e
发帖数: 172 | 2 The prob is 1. Though I have not found a good argument.
Let us do it as those ants are under random walk not brownian motion, that
will save us, and in some sense this give us a intuitive proof for the
original problem.
Let us consider only two ants. Let us consider what if an ant does not move
. It is for sure that they will meets at some time.
Okay, now expand the pentagon to a line, then if these two ants are move
independently, we can think it is equivalent to one is fixed the other has
prob |
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