6 problems

In one spatial dimension, shocks are curves generated by nonuniqueness of one-sided minimisers; pre-shocks are space-time points where new shocks are created, while shock curves ca…

For a convex Hamiltonian with associated Lagrangian $L_\omega$, generalized directed polymers are defined through the positive-viscosity dynamics, while their ground states are one…

In one spatial dimension, let $\Phi$ be the global solution with $a=b=0$, and regard it modulo additive constants so that it has stationary spatial increments. Brownian limit conje…

Assume the hypotheses of the one-force-one-solution conjecture, and work almost surely. A one-sided minimiser is a curve defined on $(-\infty,t]$ such that compact perturbations fi…

Let $d\in\mathbb{N}$ and let $F_\omega(t,x)$ have exponential decay of space-time correlations. For every $b\in\mathbb{R}^d$, consider global solutions of the random Hamilton–Jacob…

Let a renormalisation transformation act on point fields formed by concentration points and shocks, with fixed points describing the long-time geometry of minimisers and polymers.…