4 papers
Super-Arrhenius relaxation of the triangular plaquette model in any dimension
Laurent Bartholdi, Ivailo Hartarsky, Ivan Mitrofanov
Consider the following plaquette model from statistical physics: a lamp lies at every vertex of the triangular lattice and a switch lies at every even vertex of the (bipartite) dua…
Triangle covering problems and the Viterbo inequality in the plane
Alexey Balitskiy, Ivan Mitrofanov, Alexander Polyanskii
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of…
Finite dimensional amenable groups
Anna Erschler, Ivan Mitrofanov
We show that an amenable group of finite Assouad-Nagata dimension satisfies the property of Shalom. Such infinite groups are known to admit a virtual homomorphism onto $\m…
Factor Complexity of the Most Significant Digits of~
Mehdi Golafshan, Ivan Mitrofanov
We investigate unipotent dynamics on a torus and apply these techniques to the following problem. Let \(d\) be a positive integer, and let \(a > 0\) be a real number. For an intege…