Introduction to Random Walks and Markov Processes - Preparatory Lecture 1

Explore the fundamentals of statistical physics in this preparatory lecture by Abhishek Dhar from the International Centre for Theoretical Sciences. Delve into the concept of random walks as the simplest example of a Markov process. Examine continuous space-time limits, discrete space/continuous time scenarios, and probability distributions for walker positions. Learn about evolution equations for probability functions and their solutions. Investigate discrete time/space cases, tackle assignments, and understand the concept of continuous time in relation to random walks. Conclude with an introduction to the master equation, providing a solid foundation for advanced topics in statistical physics.

Preparatory Lecture 1
Random Walk - Simplest example of a Markov Process
Continuous space time limit
Space Discrete/Time Continuous
Probability that Walker is at
Evolution Equation for PX,n
Solution of the evolution equations
Homework: Try solving by double fourier transform
Discrete time/Space Case
Assignments
Time is Continuous
Master equation