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What is Range of 2D Simple Random Walk Analysis about?
This thesis investigates the range of a two-dimensional simple random walk, demonstrating that its expected size at time n is approximately cn/ log n, where c is a constant. The proof involves decomposing the range using new random variables and applying generating functions and the Tauberian theorem. The study also estimates the variance of the range, confirming the convergence of the expected range to πn/ log n in probability.
- Author
- Tanmoy Bhunia
- Language
- EN