(C) D. S. Grebenkov, Dataset created for the project INADILIC
A Brownian motion trajectory is generated as a cumulative
sum of independent Gaussian variables with mean 0 and
variance 2D, with the diffusion coefficient D set to 1.
The full set contains M = 1000 one-dimensional trajectories
of N = 10000 points (steps).
The trajectories were generated in Matlab by the function 'BM.m'
The file 'BM_sample.txt' contains a column of positions.
The file 'BM_full.mat' can be opened in Matlab by commands:
A = load('BM_full.mat'); % structure containing the trajectories
X = A.X; % matrix of size MxN, X(m,:) is the m-th trajectory
clear A;
One can check that the mean square displacement satisfies
the Einstein relation = 2Dt
plot(mean(X.^2));