### Large deviations for the intersection of two ranges

Probability Seminar

26th May 2021, 4:00 pm – 5:00 pm

online, online

It is well known that the ranges of two independent random walks on Z^d have a finite intersection almost surely if and only if d is larger than or equal to 5. Now, what about the probability that the number of points visited by the two walks exceeds a large constant t? A famous result of Khanin, Mazel, Shlosman and Sinai from the early 90’s showed that it decays like a stretched exponential with the striking exponent 1-2/d, up to arbitrarily small error in the exponent. Our main result refines this asymptotic, and answers in the discrete setup a conjecture of van den Berg, Bolthausen, and den Hollander. We will explain this, and discuss the main ideas of the proof. This is joint work with Amine Asselah.

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