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- W3014841103 abstract "Towards formulating quantum gravity, we present a novel mechanism for the emergence of spacetime geometry from randomness. In [arXiv:1705.06097], we defined for a given Markov stochastic process the distance between configurations, which enumerates the difficulty of transition between configurations. In this article, we consider stochastic processes of large-$N$ matrix models, where we regard the eigenvalues as spacetime coordinates. We investigate the distance for the effective stochastic process of one-eigenvalue, and argue that this distance can be interpreted in noncritical string theory as probing a classical geometry with a D-instanton. We further give an evidence that, when we apply our formalism to a tempered stochastic process of $U(N)$ matrix, where the 't Hooft coupling is treated as another dynamical variable, a Euclidean AdS$_2$ geometry emerges in the extended configuration space in the large-$N$ limit, and the horizon corresponds to the Gross-Witten-Wadia phase transition point." @default.
- W3014841103 created "2020-04-10" @default.
- W3014841103 creator A5050088939 @default.
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- W3014841103 date "2020-04-02" @default.
- W3014841103 modified "2023-09-26" @default.
- W3014841103 title "Emergent quantum geometry from stochastic random matrices" @default.
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- W3014841103 doi "https://doi.org/10.48550/arxiv.2004.00975" @default.
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