Analytical expressions for the first passage time distribution and hit distribution in two and three dimensions

Editor's Note: The first passage time is a commonly calculated property of diffusive processes that defines, for example, how long it takes for a random walker to travel a given distance from its origin point. Results for one-dimensional systems are commonly presented early in textbooks, especially since they demonstrate useful derivation techniques like the use of inverse Laplace transform. Here, the two- and three-dimensional problem is studied both analytically and numerically, providing a deeper understanding of useful derivation techniques for upper level graduate students.