A LOCAL CLT FOR CONVOLUTION EQUATIONS WITH AN APPLICATION TO WEAKLY SELF-AVOIDING RANDOM WALKS

作者：Avena Luca^*; Bolthausen Erwin^*; Ritzmann Christine^*

来源：Annals of Probability, 2016, 44(1): 206-234.

DOI：10.1214/14-AOP971

• Central limit theorem
• convolution equations
• self-avoiding random walks

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 continuous space. The bounds obtained are sharper than those obtained by other methods.

• 出版日期2016-1