Two DPRMs

 Consider two non-interesecting DPRMs navigating the same energy landscape:

 The non-crossing condition can be implemented by considering the two paths as world-lines of fermions:

 Occupation of the top 2 "energy levels" gives:

 Reduction in F_2 due to the non-crossing constraint (L=512):

Few DPRMs

 This pattern continues for multiple non-crossing paths.

 Similar scaling is observed for the differences between means of the top "energy differences"