Author

M. Shkolnikov

3 papers indexed here

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Preprint Jul 2026

Many-point tropical relaxation and the Monge--Amp\`ere equation

In this paper we prove that a process we call tropical relaxation gives a convergent method for numerically approximating the Monge--Amp\`ere Dirichlet problem on bounded convex planar domains. We approximate the prescribed probability measure by point clouds and construct the least concave tropical roof with zero boun...

N. Kalinin, Ernesto Lupercio, Higinio Serrano et al. · 2 citations

Preprint Aug 2026

Symmetry Emergence in Self-Organized Criticality

We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of the underlying lattice is much larger than the number of random perturbation points distributed according to a prescribed probability measure...

Ernesto Lupercio, Mikhail Shkolnikov · 0 citations

Preprint Jul 2026

Many-point tropical relaxation and the Monge--Amp\`ere equation

We prove a quantitative tropical approximation to the planar Aleksandrov Monge--Amp\`ere equation. Let $\Omega\subset\mathbb R^2$ be a bounded open convex domain, fix $K\Subset\Omega$, and let $F_N=G_{P_N}(0_\Omega)$ be the minimal nonnegative concave tropical series with integral slopes, zero boundary values, and corn...

N. Kalinin, Ernesto Lupercio, Higinio Serrano et al. · 2 citations