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Juergen Fenn <[log in to unmask]>
Tue, 8 Feb 2011 09:46:06 +0100
text/plain (24 lines)
Am 08.02.11 09:37 schrieb Juergen Fenn:

> But unfortunately I did not get any code snippets from there,

I have to correct this: You get the LaTeX source by simply copy and
pasting the formulae... it's as simple as that, e.g.:

Let {X n d }n≥0be a uniform symmetric random walk on Zd, and Π(d)
(a,b)={X n d ∈ Zd : a ≤ n ≤ b}. Suppose f(n) is an integer-valued
function on n and increases to infinity as n↑∞, and let
$$E_n^{\left( d \right)} = \left\{ {\prod {^{\left( d \right)} } \left(
{0,n} \right) \cap \prod {^{\left( d \right)} } \left( {n + f\left( n
\right),\infty } \right) \ne \emptyset } \right\}$$
Estimates on the probability of the event $$E_n^{\left( d \right)} $$
are obtained for $$d \geqq 3$$ . As an application, a necessary and
sufficient condition to ensure $$P\left( {E_n^{\left( d \right)}
,{\text{i}}{\text{.o}}{\text{.}}} \right) = 0\quad {\text{or}}\quad
{\text{1}}$$ is derived for $$d \geqq 3$$ . These extend some results
obtained by Erdős and Taylor about the self-intersections of the simple
random walk on Zd.