Global Completability with Applications to Self-Consistent Quantum Tomography |
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Authors: | Cyril Jakob Stark |
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Institution: | 1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK 2. Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK
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Abstract: | Motivated by recent developments on solvable directed polymer models, we define a ‘multi-layer’ extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture. |
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