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Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

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SRQW03 - Scaling limits & SPDEs: recent developments and future directions

We study one-dimensional decaying Burgers turbulence with the covariance of initial profile
of Gaussian-distributed velocities decaying as inverse square of the distance. Combining the
heuristic replica trick of statistical mechanics with insights from the random matrix theory we
reveal a freezing phase transition with decreasing viscosity. In the low-viscosity phase the
one-point probability density of velocities becomes non-Gaussian reflecting a spontaneous
one step replica symmetry breaking in the associated statistical mechanics problem. We
obtain the low orders velocity cumulants analytically which favourably agree with numerical
simulation. The presentation will be based on a joint work with P. Le Doussal and A. Rosso.

This talk is part of the Isaac Newton Institute Seminar Series series.

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