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We propose a technique to compute the deformation parameter of thegeneralized uncertainty principle by using the leading quantum corrections tothe Newtonian potential. We just assume General Relativity as theory ofGravitation, and the thermal nature of the GUP corrections to the Hawkingspectrum. With these minimal assumptions our calculation gives, to first order,a specific numerical result. The physical meaning of this value is discussed,and compared with the previously obtained bounds on the generalized uncertaintyprinciple deformation parameter.

GUP parameter from quantum corrections to the Newtonian potential