On the distributions of position operators on Weakly Monotone Fock Space

In this talk we investigate the distributions for sums of creation and annihilation operators on Weakly Monotone Fock Space. After obtaining a recursive formula for the moments $\mu_{m,n} := \omega_{\Omega}((\sum_{k=1}^{m}(A_{k}+A_{k}^{\dagger}))^{2n})$, where $\Omega$ is the vacuum vector and $\omega_{\Omega}$ is the vacuum expectation, we calculate the Cauchy Transform of the distribution measure.