I'm trying to show that two random walks will eventually meet in a two dimensional setting but I can't figure out where to start. Can someone lead me towards the right direction?
2026-04-06 17:49:10.1775497750
Probability related to random walks in two dimensions
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To get you started
Read http://stat.math.uregina.ca/~kozdron/Research/Talks/duke_polya.pdf
Do not analyze two random walks. Your problem can be replaced with a single random walk with:
$$P(2R)=P(2U)=P(2L)=P(2D)=\frac{1}{16}$$ $$P(1R,1U)=P(1R,1D)=P(1L,1U)=P(1L,1D)=\frac{2}{16}$$ $$P(0U,0D)=\frac{4}{16}$$
This last can be thrown away as it doesn't change the state giving
$$P(2R)=P(2U)=P(2L)=P(2D)=\frac{1}{12}$$ $$P(1R,1U)=P(1R,1D)=P(1L,1U)=P(1L,1D)=\frac{2}{12}$$
Please post your solution.