{"id":357740,"date":"2017-01-25T13:19:35","date_gmt":"2017-01-25T21:19:35","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/?post_type=msr-research-item&p=357740"},"modified":"2018-10-16T20:00:40","modified_gmt":"2018-10-17T03:00:40","slug":"self-interacting-random-walks","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/self-interacting-random-walks\/","title":{"rendered":"Self-Interacting Random Walks"},"content":{"rendered":"

Let \u03bc<\/span>1<\/span><\/span>,<\/span>.<\/span>.<\/span>.<\/span>\u03bc<\/span>k<\/span><\/span><\/span><\/span><\/span> be d<\/span><\/span><\/span><\/span>-dimensional probability measures in $\\R^d$<\/span><\/span><\/span> with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.<\/p>\n","protected":false},"excerpt":{"rendered":"

Let \u03bc1,…\u03bck be d-dimensional probability measures in $\\R^d$ with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. 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