The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe$_2$ obtained by mechanical exfoliation on a Si/SiO$_2$ substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times $t$ exceeding $sim$50 ps after the excitation pulse, is described by a dependence of the form $1/(t+t_0)$. Photoluminescence decay is accelerated with a decrease in temperature, as well as with a decrease in the energy of emitting states. It is shown that the observed dynamics cannot be described by a bimolecular recombination process, such as exciton--exciton annihilation. A model that describes the nonexponential photoluminescence dynamics by taking into account the spread of radiative recombination times of localized exciton states in a random potential gives good agreement with experimental data.
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