Revisiting Brownian SYK and its possible relations to de Sitter

We revisit Brownian Sachdev-Ye-Kitaev model and argue that it has emergent energy conservation overlooked in the literature before. We solve this model in the double-scaled regime and demonstrate hyperfast scrambling, exponential decay of correlation functions, bounded spectrum and unexpected factorization of higher-point functions. We comment on how these results are related to de Sitter holography.