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On the location of the 1-particle branch of the spectrum of the disordered stochastic Ising model

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  • We analyse the lower non trivial part of the spectrum of the generator of the Glauber dynamics for a $d$-dimensional nearest neighbour Ising model with a bounded random potential. We prove conjecture 1 in [1]: for sufficiently large values of the temperature, the first band of the spectrum of the generator of the process coincides with a closed non random segment of the real line.
    Mathematics Subject Classification: Primary: 82B44; Secondary: 60K35.


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