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In this work we study of the dynamics of large size random neural networks.
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Causality requires that the inverse of the operator d / d t d/dt vanishes for t < 0 t<0 so that the solution of ( d / d t ) h = f ( h ) (d/dt)h=f(h) depends on the value of h ( t ) h(t) at previous time. The term δ = 0 + \delta=0^{+} ensures that ∂ a − 1 = e − δ t a θ ( t a ) \partial_{a}^{-1}=e^{-\delta t_{a}}\theta(t_{a}) , where θ ( t ) \theta(t) is the Heaviside theta function
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