Results for the 2D Self-Trapping Random Walk
|Average number of steps before termination:
|Average number of failed attempts:
|Number of walks in simulation
Probability density for the number of steps before trapping occurs
Examples for walks with the maximum number of constrained steps
Conjecture: A n-step 2D STW has never more than n-floor(sqrt(4*n+1))-2 steps
with only two choices for the possible next direction.
n-floor(sqrt(4*n+1) is Sequence
A076874 in Sloane's OEIS.
5 Unconstrained and 7 maximally 2-constrained walks of length 10
Manhattan Distance Start-End for n-step Self-Avoiding Walks
Asymptotic Behavior of Mean Square Displacement
Asymptotic Behavior of Mean Manhattan Displacement
End-to-End Euclidean Distance Distribution of all 25-Step Walks
Results of simulation, comparison with exact probabilities
Count self-trapping walks up to length 23
Enumeration of all short self-trapping walks
Distribution of end point distance
Average Euclidean and squared end point distance
Average Manhattan end point distance
Comparison of average Euclidean and Manhattan displacements
Unsolved Problem: Is there an asymptotic
value for the difference between the average
displacement of all self-avoiding n-step walks and the subset of self-trapping n-step
walks for large n.
See figure: Manhattan displacement difference SAW-STW.
Fortran program to determine exact probabilities
Fortran program for distance counting