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Tuesday, March 30, 2021

**Abstract:** Multi-species Sherrington-Kirkpatrick Spin glass model, as an inhomogeneous generalization of classical SK model, was first introduced by Barra etal in 2015, later Panchenko set up the Parisi formula to compute limiting free energy at all temperatures. However, all those results can only hold when the disorder variance matrix is positive semi-definite. For the indefinite MSK model, nearly nothing rigorous is known, physicists conjectured that this model has some intrinsic difference with the positive definite case. In this talk, we will discuss some fluctuation results for the general MSK model in replica symmetric regime. First, A unified argument for the exponential concentration of overlap will be presented, and this concentration result further enables one to prove a CLT of free energy. Besides that, we also introduce a new species-wise cavity approach to study the fluctuation of overlap vectors, and this approach does not require positive definite assumption. The fluctuation results also suggest the phase boundary (known as AT line) of replica symmetry and replica symmetry breaking for general MSK model, we will conclude with an explicit form of conjectured AT equation.