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A local CLT for convolution equations with an application to weakly self-avoiding random walks. (English) Zbl 1343.60009

Authors’ abstract: We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application, we treat such self-avoiding walks in a continuous space. The obtained bounds are sharper than those obtained by other methods.

MSC:

60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

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