Synchronous update revisited

red ball Directed Paths in Random Media (DPRM): Stochastic Cole-Hopf transformation is equivalent to a path integral

yellow ballZero temperature limit corresponds to least energy paths, which can be obtained recursively (transfer matrix, dynamic programming)

yellow ballSynchronous growth with variable size is equivalent to DPRM leads to similar statistics of sectors and ancestry:

yellow ball"Evolution in range expansions with competition at rough boundaries,"

S. Chu, M.Kardar, D.R. Nelson, & D.A. Beller, Journal of Theoretical Biology 478, 153 (2019). (off-line)

red ballFitness and Mutation may serve as an alternative interpretation for optimal energy and random landscape:

yellow ball What is the distribution of fitness at the front of range expansion?       

yellow ball The stepping stone model predics a (non-Gaussian) Tracy-Widom distribution:       

yellow ball Different fitness distributions are likely for different areas of competition:      

yellow ball "The  Mother Machine"

 

versus

yellow ball "The Long term evolution experiment"