Emergence of extreme events from randomly chirped condensate

We explore rogue wave emergence in generic wave systems governed by the nonlinear Schrödinger equation. We highlight the interplay between the stochastic focusing induced by a random chirp of a continuous wave condensate and modulation instability of the condensate to periodic and/or random perturbations. We show that regardless of its statistical properties, the random chirp of the condensate leads to a non-Gaussian, heavy-tailed probability density distribution of peak powers of the waves excited atop of the condensate, which is a statistical signature of rogue waves, or more broadly, extreme events in physics. • Modulation instability and random external driving aid extreme event excitation. • The chirp sign dictates the convergence or divergence of generated breathers. • Random chirped condensate incites the emergence of rogue waves. • Extreme waves are indifferent to random chirped condensate's statistical properties.