# Random walk in a sphere

Given a sphere of radius $R$, divided in cubic cells of size $l$, the probability for a particle to jump from a cube to another adiacent is: $P=\frac{1}{6}$. If we define the probability to exit from the sphere as: $P_0(l,R,t)$ what is the expression for this probability vs. time $t$, radius $R$ and cell's size $l$? We can consider for the particle to be outside the sphere when it occupies a cell with the center greater than $R$. The starting point of the process is the center of the sphere and the first cubic cell is located such that its center coincides with the center of the sphere itself. Thanks.

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