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In the ergodic theory of semi-dispersing billiards the Local Ergodic Theorem,proved by Chernov and Sinai in 1987, plays a central role. So far, all existingproofs of this theorem had to use an annoying global hypothesis, namely thealmost sure hyperbolicity of singular orbits. (This is the so calledChernov--Sinai Ansatz.) Here we introduce some new geometric ideas to overcomethis difficulty and liberate the proof from the tyranny of the Ansatz. Thepresented proof is a substantial generalization of my previous joint resultwith N. Chernov (which is a $2D$ result) to arbitrary dimensions.  An important corollary of the presented ansatz-free proof of the LocalErgodic Theorem is finally completing the proof of the Boltzmann--Sinai ErgodicHypothesis for hard ball systems in full generality.

The Boltzmann--Sinai Ergodic Hypothesis In Full Generality