Questions about the Billard Walk Implementation

[GrenteTheo]

Dear contributors of the volesti project,

In the develop branch of the volesti deposit, more precisely in volesti/include/random_walks, I was wondering why the length (the variable T) computed in the file https://github.com/GeomScale/volesti/blob/develop/include/random_walks/uniform_billiard_walk.hpp#L102 and in the file https://github.com/GeomScale/volesti/blob/develop/include/random_walks/uniform_accelerated_billiard_walk.hpp#L102 are not the same. In the first file, T=uniformL and in the second T=-log(uniform)L, shouldn't this two length be generated in the same manner ?

I am also wondering why not take for T the square root of -log(uniform)*L in order to obtain a gaussian distribution on the coordinates ? Is there a particular reason to stick to an exponential distribution ?

[vissarion]

You should treat the length of the trajectory in the billiard walk as a heuristic, therefore yes it could be the square root of -log(uniform)*L or some other function. Ideally, the function should be a parameter of the walk such that the user can define their own functions. Now regarding the first billiard walk you mention it is redundant and we should consider removing it.

[GrenteTheo]

Thank you for your answer ! It confirmed my thoughts on the choice of the length of the trajectory as nothing more than an heuristic.