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Rosengren and Schlosser introduced notions of ${\it R}_N$-theta functions forthe seven types of irreducible reduced affine root systems, ${\it R}_N={\itA}_{N-1}$, ${\it B}_{N}$, ${\it B}^{\vee}_N$, ${\it C}_{N}$, ${\itC}^{\vee}_N$, ${\it BC}_{N}$, ${\it D}_{N}$, $N \in \mathbb{N}$, and gave theMacdonald denominator formulas. We prove that, if the variables of the ${\itR}_N$-theta functions are properly scaled with $N$, they construct seven setsof biorthogonal functions, each of which has a continuous parameter $t \in (0,t_{\ast})$ with given $0< t_{\ast} < \infty$. Following the standard method inrandom matrix theory, we introduce seven types of one-parameter ($t \in (0,t_{\ast})$) families of determinantal point processes in one dimension, inwhich the correlation kernels are expressed by the biorthogonal thetafunctions. We demonstrate that they are elliptic extensions of the classicaldeterminantal point processes whose correlation kernels are expressed bytrigonometric and rational functions. In the scaling limits associated with $N\to \infty$, we obtain four types of elliptic determinantal point processeswith an infinite number of points and parameter $t \in (0, t_{\ast})$. We givenew expressions for the Macdonald denominators using theKarlin--McGregor--Lindstr\"om--Gessel--Viennot determinants for noncollidingBrownian paths, and show the realization of the associated ellipticdeterminantal point processes as noncolliding Brownian brides with a timeduration $t_{\ast}$, which are specified by the pinned configurations at time$t=0$ and $t=t_{\ast}$.

Macdonald denominators for affine root systems, orthogonal theta functions, and elliptic determinantal point processes