Probability distributions for directed polymers in random media with correlated noise

Understand

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution.

• We inquire if and how this universal distribution is modified in the presence of spatially correlated noise.
• The width of the distribution scales as the DPRM length to an exponent $\beta$, in good (but not full) agreement with previous renormalization group and numerical results.
• The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent.