We prove that the Beta random walk, introduced in [BC17] 2017, has cubic fluctuations from large deviation principle of GUE Tracy-Widom type for arbitrary values ?>0 and ?>0 parameters distribution, removing previous restrictions on their values. Furthermore, we still hold intermediate disorder regime. also show any walk space-time environment matches certain moments with As a corollary emergen...

We describe a method for constructing a model of second order dependent type theory out of a model of classical second order predicate logic. Apart from the construction being of interest by itself, this also suggests a way of proving the completeness of the formulas-as-types embedding from second order predicate logic to second order dependent type theory. Under this embedding, formulas are in...