The expected distance from origin after a random walk of $N$ steps in a $d$ dimensional space, is close to $$\sqrt{\dfrac{2N}{d}}\dfrac{\Gamma\left(\dfrac{d+1}{2}\right)}{\Gamma\left(\dfrac{d}{2}\right)}$$ for very large $N$. This was mentioned here. I would be very obliged if someone can mention to me a reference (bibliographic) to an article, book or any publication, where this expression was derived or mentioned. Please restrict to references, and not explanation of the formula itself.
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The expression was given by "Henry" to a question by "Diego" in january 2012. Is it possible to have the source of this Formula? – Picard Porath Sep 01 '13 at 11:36
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You might try to ping Henry under his answer, to see, whether he knows about a reference. – Martin Sleziak Sep 01 '13 at 12:22
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@ Martin Sleziak, thanks a lot. Unfortunately I am not qualified to add a comment to the old answer. Do you have an idea how can I contact Henry on the subject. Any help will be highly appreciated. – Picard Porath Sep 01 '13 at 14:22
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3For those seeking for the reference > 4 years after the question was asked, here is a 2011 paper with explicit computations: https://pdfs.semanticscholar.org/8e6b/03f71b0bd3e38b50dde5f6a36a9a7ae91183.pdf – Kolya Ivankov Dec 15 '17 at 06:40