Topic: Simple Random Walks on the Integers

Symmetry and Reversal of Walk Paths

Return Probabilities at Even Times

Proving the Ballot Theorem

Positive Bridges and Dyck Paths

Parity and Lattice Constraints

Joint Probabilities of the Endpoint and Maximum

First-Return Time Probabilities

Encoding Paths by Their Up-Steps

Deriving the Occupation-Time Arcsine Law

Defining the Simple Symmetric Walk