##### Department of Mathematics,

University of California San Diego

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### Algebra Colloquium

## Filippo Tolli

#### Universita Roma Tre

## Harmonic analysis of finite lamplighter random walks

##### Abstract:

Recently, a lot of papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. In the present talk, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the $C_2$-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. In the case the graph has a transitive isometry group $G$, we also describe the spectral analysis in terms of the representation theory of the wreath product $C_2\wr G$. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples were already studied by Haggstrom and Jonasson by probabilistic methods.

Host: Efim Zelmanov

### November 13, 2006

### 2:00 PM

### AP&M 7218

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