Probability distribution functions in the finite density lattice QCD

We study the phase structure of QCD at high temperature and density by lattice QCDsimulations adopting a histogram method. We try to solve the problems which arise in the numerical study of the finite density QCD, focusing on the probability distributionfunction (histogram). As a first step, we investigate the quarkmass dependence and the chemical potentialdependence of the probability distributionfunction as a function of the Polyakov loop when all quarkmasses are sufficiently large, and study the properties of the distribution function. The effect from the complex phase of the quarkdeterminant is estimated explicitly. The shapeof the distribution functionchanges with the quarkmass and the chemical potential. Through the shapeof the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quarkregion is determined for the 2+1-flavor case.