Fluctuation and relaxation properties of pulled fronts: a possible scenario for non-Kardar-Parisi-Zhang behavior

We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1\mathrm{/}t$ velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is the appropriate effective long-wavelength low-frequency theory in this regime. Simulations in 2$D$ confirm the proposed scenario, and yield exponents $\beta \approx 0.29\pm 0.01$, $\zeta \approx 0.40\pm 0.02$ for fluctuating pulled fronts, instead of the KPZ values $\beta =1\mathrm{/}3$, $\zeta = 1/2$\mathrm{.}Ourvalueof$\beta$ is consistent with an earlier result of Riordan {\em et al.}