Author

M. Shkolnikov

2 papers indexed here

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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