The previous post ran a simulation of one-dimensional random walk. Here is the MATLAB code that was run to achieve the the results, along with explanatory documentation:
numRuns = 100000; %# of resets to position 0
numTrials = 1000000; %# of trials per run
probLeft = 0.5; %Here, equal probability going to left and right
zero = 0; %# of times on position 0
negative = zeros(1); %Array to keep track of # of times on negative numbers
positive = zeros(1); %Similar array for positive numbers
for run = 1:numRuns %Loop over the # of runs
position = 0; %Reset position for each run
for count = 1:numTrials %Loop iver the # of trials
roll = rand; %Simulated roll
if roll < probLeft %Going to the left
position = position - 1;
else %Going to the right
position = position + 1;
end
if position < 0
if abs(position) > length(negative) %If the position has never been visited before
negative(abs(position)) = 0; %Initialize the value to avoid error
end
negative(abs(position)) = negative(abs(position)) + 1; %Increase counter
elseif position > 0
if position > length(positive) %Similar tasks as above, but for positive positions
positive(position) = 0;
end
positive(position) = positive(position) + 1;
else
zero = zero + 1; %If landed on zero
end
end
end
y = [negative(end:-1:1) zero positive]; %# of times landed on each position
x = -length(negative):length(positive); %Position vector
plot(x,y)
xlabel('Position')
ylabel('Number of Times on the Position')
title('1 Dimensional Random Walk')
In this code, the variable 'probLeft' had a constant value of 0.5, reflecting on equal probability of going to the left and right. Further adjustments can tweak to define this variable to allow for the probability to reflect on the current position.
