Poincar\'{e} and Weak Poincar\'{e} Inequalities for the Mixed Poisson   Measures
  By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincar\'{e} and weak Poincar\'{e} inequalities are established, while another Poincar\'{e} type inequality is disproved under some reasonable assumptions. 
Chang-Song Deng
math.PR