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Continuous-time weakly self-avoiding walk on Z has strictly monotone escape speed

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SSDW01 - Self-interacting processes

Weakly self-avoiding walk is a model of simple random walk paths that penalizes self-intersections. On Z, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS —Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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