# Control of fluctuations and heavy tails for heat variation in the two-time measurement framework. (arXiv:1802.02073v1 [math-ph])

perturbations, we give sufficient ultraviolet regularity conditions on the

perturbation for the moments of the heat variation to be uniformly bounded in

time, and for the Fourier transform of the heat variation distribution to be

analytic and uniformly bounded in time in a complex neighborhood of 0. On a set

of canonical examples, with bounded and unbounded perturbations, we show that

our ultraviolet conditions are essentially necessary. If the form factor of the

perturbation does not meet our assumptions, the heat variation distribution

exhibits heavy tails. The tails can be as heavy as preventing the existence of

a fourth moment of the heat variation.