126 citations · 619 across the 30 of their papers we have counts for
Showing 2017 · math.APShow all
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math.AP2017★ 14 cited
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
Grégory Dumont, Pierre Gabriel
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical…
math.AP2017★ 62 cited
Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
Vincent Bansaye, Bertrand Cloez, Pierre Gabriel
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of cons…
math.AP2017★ 37 cited
Measure solutions to the conservative renewal equation
Pierre Gabriel
We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality app…