Classical and Quantum walks
Student No.:50
Time:13:00-14:50 2017-4-25/4-27/4-28, 15:10-17:00 2017-4-26
Instructor:Alberto Grunbaum  [UC Berkeley]
Place:Conference room 1, 2017-4-25/4-27/4-28; Conference room 3, 2017-4-26
Starting Date:2017-4-25
Ending Date:2017-4-28


We will discuss recurrence properties of the standard walk in dimensions 1,2 and 3. A brief look at Brownian motion and the Feynman- Kac formula. We will discuss quantum walks and their
recurrence properties. A look at the Parrondo paradox.

This short course will differ from more standard ones. I will try to exhibit some of the connections with real and complex analysis and partial differential equations.

In each lecture some piece of analysis will play a useful role:

Lect 1.  The gambler's ruin problem and difference equations.

Lect 2.  The renewal equation and generating functions

Lect 3.   A look at the Feynman-Kac formula that Cauchy could understand.

Lect 4.   Quantum walks as an extension of Fourier series.





Basic linear algebra, Basic analysis



D. Stroock     An introduction to Markov processes, Springer

J. Lamperti     Probability theory, Benjamin