Generalized uncertainty principle and asymptotically safe gravity

We present a procedure to link the deformation parameter \beta of the generalized uncertainty principle (GUP) to the two free parameters \omega and \gamma of the running Newtonian coupling constant of the asymptotically safe gravity program. To this aim, we compute the Hawking temperature of a black hole in two different ways. The first way involves the use of the GUP in place of the Heisenberg uncertainty relations, and therefore we get a deformed Hawking temperature containing the parameter \beta . The second way involves the deformation of the Schwarzschild metric due to the Newtonian coupling constant running according to the asymptotically safe gravity prescription. The comparison of the two techniques yields a relation between \beta and \omega, \gamma. As a particular case, we discuss also the so-called \zeta -model. The relations between \beta and ˜ omega, \zeta allow us to transfer upper bounds from one parameter to the others.