2D random Walker Mean displacement vectors plotting

Benjamin Puzantian

2019 2 2

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I am trying to plot the mean squre vectors x_n that is the number of steps in the x-direction and y_n that is the number of steps in the y-direction as a function of M the number of steps by a walker. N is the number of walkers. This is a 2D random walker on a square lattice problem. What code should I use? Thank you

clc;
clearvars;
N = 10; 
M = 10; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;
for m=1:M
  for n = 1:N % Looping all values of N into x_t(n).
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    x_t(n+1) = x_t(n) + A;
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    y_t(n+1) = y_t(n) + A;
  end
  plot(x_t, y_t);
  
  hold on
  pot([0:M],x_t)
  
  hold on
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

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Benjamin Puzantian 2019-2-2

The quesiton asks:

Write a program that performs M random walks of N steps in two dimensions on a square lattice, assuming that each step is chosen at random, and each of the four possible directions are equally probable.

Run the program for M~1000 walkers who are all originally at the origin. Allow the walkers to take at least 1000 steps.

Use a plotting program to draw maps of several independent random walks and discuss.

Compute the mean displacement vector by ensemble averaging xN and yN over the M random walks, for different values of N. Plot as a function of N.

xN is the mean dispalcement of the x fromt he orgin by the walker

Walter Roberson 2019-2-2

If randn were capable of infinite precision ,then the probability of generating an exact 0 would be mathematically 0 (as in 1 out of infinity, not as in 0 out of infinity.) However, randn is not capable of infinite precision, and so 0 does end up with a slightly higher probability than any other representable number. Still very small.

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