A gradient model for the Bernstein polynomial basis

We introduce a symmetric, gradient exclusion process within the class of non-cooperative kinetically constrained lattice gases, modelling a non-linear diffusivity in which the exchange of occupation values between two neighbouring sites depends on the local density in specific boxes surrounding the pair. The existence of such a model satisfying the gradient property is the main novelty of this work, filling a gap in the literature regarding the types of diffusivities attainable within this class of models. The resulting dynamics exhibits similarities with the Bernstein polynomial basis and generalises the Porous Media Model. We also introduce an auxiliary collection of processes, which extend the Porous Media Model in a different direction and are related to the former process via an inversion formula.