Program
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

Description:


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.

 


 

Prerequisite:

 

Basic linear algebra, Basic analysis

 


Reference:


D. Stroock     An introduction to Markov processes, Springer


J. Lamperti     Probability theory, Benjamin