##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics Seminar

## Mike Cranston

#### UC Irvine

## Self-adjoint extensions, point potentials, and pinned polymers

##### Abstract:

In this talk we discuss closed self adjoint extensions of the Laplacian and fractional Laplacian on $L^2$ of Euclidean space minus the origin. In many cases there is a one parameter family of these operators that behave like the original operator plus a potential at the origin. Using these operators, we can construct polymer measures which exhibit interesting phase transitions from an extended state to a bound state where the pinning at the origin due to the potential takes over. The talk is based on joint works with Koralov, Molchanov, Squartini and Vainberg.

Host: Jason Schweinsberg

### February 27, 2014

### 9:00 AM

### AP&M 6402

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