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Loop-weighted walk

Mathematical Physics & Probability

Speaker: Tyler Helmuth, University of British Columbia
Location: 2112 MSB
Start time: Mon, Nov 17 2014, 2:10PM

Loop-weighted walk is a one-parameter family of non-Markovian random walks that arise naturally in statistical mechanics. A loop-weighted walk receives weight lambda^k if it contains k loops; whether this is a reward or punishment depends on the value of the parameter lambda. A challenging feature of the model is that it is not purely repulsive, meaning the weight of the future of a walk may either increase or decrease if the past is forgotten. Repulsion is typically an essential property for lace expansion techniques; despite this I will explain how the lace expansion can be used to prove that loop-weighted walk is diffusive in high dimensions.