Maximal entropy random walk and quantum mechanics

[Jarek Duda]

While introducing random walk on given graph, we usually assume that
for each vertex, each outgoing edge has equal probability. This random
walk usually emphasize some path. If we work on the space of all
possible paths, we would like to have uniform distribution among them
to maximize entropy. It occurs that we can introduce random walk which
fulfills this condition: in which for each two vertexes, each path
between them of given length has the same probability.
Probability of going from a to b in MERW is
S_ab= (1/lambda) (psi_b/psi_a)
where lambda is the dominant eigenvalue of adjacency matrix, psi is
corresponding eigenvector. Now stationary probability distribution is
p_a is proportional to psi_a^2

We can generalize uniform distribution among paths into Boltzmann
distribution and finally while making infinitesimal limit for such
lattices covering R^n, we get behavior similar to quantum mechanics.
This similarity can be understand that QM is just a natural result of
four-dimensional nature of our world
http://arxiv.org/abs/0910.2724
In this paper further generalizations are made in classical field of
ellipsoids as its topological excitations. Their structure occurs to
be very similar to known from physics with the same spin, charge,
number of generations, mass gradation, decay modes, electromagnetic
and gravitational interaction.

What do you think about it?