To be honest, I don't believe a Boltzmann Brain is possible...
But that's only my belief- I don't think the universe is that bizarre- so I guess I believe that the universe has a beginning and end, so no infinite time and space to allow the infinitely unlikely Boltzmann Brain... or if the universe does become infinite it does so in a way that makes such an event impossible...
Mainly I found it fascinating that such a bizzare concept was used (with some controversy) in cosmology to evaluate various cosmological models.
http://arxiv.org/abs/1505.02780
http://arxiv.org/pdf/1508.01017.pdf
https://www.newscientist.com/article/mg22229692-600-quantum-twist-could-kill-off-the-multiverse/