Abstract
So far we have studied two kinds of random systems whose probability laws are expressed using the theta function. One of them is a family of one-dimensional stochastic processes consisting of seven types of noncolliding Brownian bridges. Another one is a family of two-dimensional point processes consisting of seven types of DPPs on $$\mathbb {T}^2$$ . In this last chapter, we will address future problems concerning these two families of random systems. For the former systems, the key aspect of future direction will be dynamical property of DPPs. For the latter systems, it will be the connections to other statistical systems such as the one-component plasma models and the Gaussian free fields.
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