  This paper is devoted to diffusion limits of linear Boltzmann equations. When
the equilibrium distribution function is Maxwellian distribution, it is well
known that for an appropriate time scale, the small mean free path limit gives
rise to a diffusion equation. In this paper, we consider situations in which
the equilibrium distribution function is a heavy-tailed distribution with
infinite variance. We then show that for an appropriate time scale, the small
mean free path limit gives rise to a fractional diffusion equation.

Analysis of PDEs