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 January 26th, 2011, 08:33 AM #1 Newbie   Joined: Jun 2010 Posts: 11 Thanks: 0 Random Walk question I've had a question about random walks ravaging me for the last week or so... well, a couple actually. The walk takes place on a square lattice on an infinite plane. Each step, the walk can move 1 grid unit on either the X or Y axis. I have two points, origin and some point (x,y). What is the probability that after t steps the walk is at (x,y) for the first time? What is the average value of t when the walk reaches (x,y) for the first time? I just don't understand probability well enough to formulate this, and as such I have been resorting to graphing the possibilities out. This gets exponentially more tedious and prone to error with each step of t. Any help? January 26th, 2011, 08:36 AM #2 Newbie   Joined: Jun 2010 Posts: 11 Thanks: 0 Re: Random Walk question I should probably request a transfer to College Mathematics. I missed the difference between the sections in my anxiety. January 26th, 2011, 08:46 AM #3 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Random Walk question The following link will lead to material that may be of interest: http://en.wikipedia.org/wiki/Infinite_monkey_theorem January 26th, 2011, 11:40 AM #4 Newbie   Joined: Jun 2010 Posts: 11 Thanks: 0 Re: Random Walk question The probability P that the walk is at a point (x,y) at time t is given by P(t) = (t choose ((x+y+t)/2)) * (t choose ((x-y+t)/2)) / 4^t The probability K that at time t the walk is at point (x,y) for the first time is given by: K(t) = (1-P(0)) * (1-P(1)) * (1-P(2)) * ... * (1-P(t-1)) * P(t) Now I need to simplify this to cope with the exponential growth of significant factors, since the most likely length is ~x^2+y^2 (consistent with the mean square distance from origin of a random walk being ~sqrt(t)) Tags question, random, walk Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post JoeWright Advanced Statistics 0 February 16th, 2014 04:43 PM rooney_hunter Real Analysis 0 May 13th, 2013 10:29 AM rooney_hunter Advanced Statistics 0 May 13th, 2013 04:24 AM Hayoota Advanced Statistics 1 September 28th, 2009 01:37 PM terry Advanced Statistics 3 September 16th, 2008 04:29 PM

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