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000300993 0881_ $$aDESY-16-104; IFT-UAM-CSIC-16-053; arXiv:1606.07768
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000300993 1001_ $$aPedro, Francisco Gil$$b0
000300993 245__ $$aNon-Equilibrium Random Matrix Theory : Transition Probabilities
000300993 260__ $$c2016
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000300993 520__ $$aIn this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
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000300993 7001_ $$0P:(DE-H253)PIP1013212$$aWestphal, Alexander$$b1$$eCorresponding author$$udesy
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