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As an image of the many-to-one map of loop-erasing operation $\LE$ of randomwalks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk(LERW) model is the statistical ensemble of SAWs such that the weight of eachSAW $\zeta$ is given by the total weight of all random walks $\pi$ which areinverse images of $\zeta$, $\{\pi: \LE(\pi)=\zeta \}$. We regard the Brownianpaths as the continuum limits of random walks and consider the statisticalensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of theLERW model. Following the theory of Fomin on nonintersecting LERWs, weintroduce a nonintersecting system of $N$-tuples of LEBPs in a domain $D$ inthe complex plane, where the total weight of nonintersecting LEBPs is given byFomin's determinant of an $N \times N$ matrix whose entries are boundaryPoisson kernels in $D$. We set a sequence of chambers in a planar domain andobserve the first passage points at which $N$ Brownian paths $(\gamma_1,...,\gamma_N)$ first enter each chamber, under the condition that the loop-erasedparts $(\LE(\gamma_1),..., \LE(\gamma_N))$ make a system of nonintersectingLEBPs in the domain in the sense of Fomin. We prove that the correlationfunctions of first passage points of the Brownian paths of the present systemare generally given by determinants specified by a continuous function calledthe correlation kernel. The correlation kernel is of Eynard-Mehta type, whichhas appeared in two-matrix models and time-dependent matrix models studied inrandom matrix theory. Conformal covariance of correlation functions isdemonstrated.

Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts