  An analytical solution for the optical efficiency of a luminescent solar
concentrator is presented. Due to a large number of input parameters and their
complex effect on the device efficiency numerical simulations have been
previously used for this purpose. The formulas, provided here, derived using a
probabilistic approach, significantly reduce the complexity of the problem. The
equations were validated by simulations and the obtained explicit expressions
provide a clear common ground for the theoretical description of such devices.
Implementation by a computer algebra program yields instant results for any set
of input parameters. It allows a higher level of analysis, where an inverse
task of finding parameters for a given efficiency can be readily solved.
