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L = 1. (5 points] The “drunkard's walk” is a classic problem in statistical physics and a simple model for Brownian moti
Posted: Thu May 12, 2022 2:28 pm
by answerhappygod
- L 1 5 Points The Drunkard S Walk Is A Classic Problem In Statistical Physics And A Simple Model For Brownian Moti 1 (93.54 KiB) Viewed 32 times
L = 1. (5 points] The “drunkard's walk” is a classic problem in statistical physics and a simple model for Brownian motion. Consider a particle that starts at the origin and takes N steps of unit length. Each step has equal probability to be to the left or to the right. Call NR and Ni the number of steps taken to the right and to the left (NR+ Nư = N). The distance from the origin is X = NR – N1. (a) Find P(X, N), the probability that the particle is at position X after N steps. Hint: Picture sequences of the form LRRLL ... RR. Count the total number of possible sequences and the number of possible sequences that result in the particle being at a distance X. (b) What is the probability that the particle is at the origin after N = 100 steps?