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Abstract
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In probability theory, the Kolmogorov 0-1 law plays an important role. In this talk, I will introduce the Kolmogorov 0-1 law in the setting of determinantal point processes. We recently proved that all determinantal point processes with self-adjoint correlation kernels satisfy the Kolmogorov 0-1 law. Our proof works in full generality and covers all the previous progresses in this direction. The crucial ingredient in our proof is the construction of operator-valued martingales. The talk is based on a recent joint work with Alexander Bufetov and Alexander Shamov.
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