## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE

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 Sender: Mailing list for the LaTeX3 project <[log in to unmask]> Date: Tue, 8 Feb 2011 09:46:06 +0100 Reply-To: Mailing list for the LaTeX3 project <[log in to unmask]> Message-ID: <[log in to unmask]> Content-Transfer-Encoding: 8bit From: Juergen Fenn <[log in to unmask]> Content-Type: text/plain; charset=UTF-8 In-Reply-To: <[log in to unmask]> Organization: juergenfenn.de MIME-Version: 1.0 Parts/Attachments: 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. Regards, Jürgen.