# Hopping particles, generating functions and the kernel method

#### Hopping particles, generating functions and the kernel method

- Event time: 11:30am until 12:30pm
- Event date: 3rd October 2018
- Speaker: Professor Richard Blythe (School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Many paradigmatic model systems in nonequilibrium statistical physics involve particles that hop between sites of a lattice. The master equation that governs the time evolution of the probability distribution for the system takes the form of a set of difference equations, which in turn can (sometimes) be solved using generating functions (essentially, the discrete analogue of a Laplace transform). The kernel method provides one technique to manipulate generating functions and determine the desired probability distribution. I will expose the machinery of the kernel method with reference to a very simple particle hopping model, and then sketch out its application to the more complex problem of interacting run-and-tumble particles.

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