【摘 要】
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The generating function G for the return probabilities in a ddimensional face-centered cubic lattice satisfies an ODE whose order grows quadratically with d
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The generating function G for the return probabilities in a ddimensional face-centered cubic lattice satisfies an ODE whose order grows quadratically with d.Until recently only the ODEs for di=7 were known; using a recursive method for computing the coefficients of G,proposed by Zenine,Hassani,Maillard,we are able to go up to d=11.These ODEs share many remarkable properties which we shall discuss in this talk.
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