Pesudo random numbers for the Landau and Vavilov distributions
The Landau distribution is the distribution with the Laplace transform \(\exp(s\ln(s))\). It is a stable distribution with parameters (1,1). The Vavilov distribution has the Laplace transform \[ \exp(s\ln(s)+\kappa(1-E_2(s/\kappa))+ \kappa\beta^2(\gamma+\ln(s/\kappa)+E_1(s/\kappa))), \] where \(E_p(x)=\int_1^\infty\exp(-x\xi)\xi^{-p} d\xi\), \(p>0\). It is an infinitely divisible distribution. The author considers different methods of pseudo-random number generation with Landau and Vavilov distributions based on the stability and infinite divisibility properties. Special attention is paid to the case where the generator starts from some \(\beta\) and then should continue with a new smaller \(\beta\) (energy decay). The Kölbig-Schorr and Rotondi-Montaga generation methods require costly reinitialization in this case. The author proposes a technique which allows to perform such simulation without reinitialization.
scientific article; zbMATH DE number 1878603
scientific article