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### Description

The study of the dynamics of occupation time has a variety of applications. For ex-

ample, it has been used to analyze the morphological dynamics of interfaces, analysis

of the fluorescence intermittency emitting from colloidal semiconductor dots, optical

imaging etc to name a few. The occupation time dynamics have been studied for

numerous problems in the context of non-equilibrium systems. In this work we study

the large deviation statistics of occupation fraction of N non-crossing Brownian par-

ticles in a certain interval. Using the extension of the Donsker-Varadhan formalism

we solve this problem by mapping it to N non-interacting spinless fermions trapped

in a square well potential. We study the behaviour of the large deviation function for

all N ≥ 1. For N = 1, the single Brownian motion in presence of a drift is known to

exhibit dynamical phase transition of first order where the large deviation function

shows singularity. For any N ≥ 2, we interestingly find that the system undergoes

multiple dynamical phase transitions of second order. This phenomenon is entirely

different from what is found for a single Brownian motion occupation fraction. Here

each transition denotes different numbers of particle occupations near the vicinity of

the interval.