A Gelfand–Tsetlin scheme of depth NN is a triangular array with mm integers at level mm,
m= 1, ..., N m= 1,…, N, subject to certain interlacing constraints. We study the ensemble of …

We study large-scale height fluctuations of random stepped surfaces corresponding to
uniformly random lozenge tilings of polygons on the triangular lattice. For a class of …

We consider the four-vertex model with a special choice of fixed boundary conditions giving
rise to limit shape phenomena. More generally, the considered boundary conditions relate …

Plane partitions naturally appear in many problems of statistical physics and quantum field
theory, for instance, in the theory of faceted crystals and of topological strings on Calabi–Yau …

We introduce elliptic weights of boxed plane partitions and prove that they give rise to a
generalization of MacMahon's product formula for the number of plane partitions in a box …

Geometrical frustration arises when the lattice geometry prevents local interaction energies
from minimizing simultaneously. Whether and how geometrically frustrated spins or charges …

We investigate the properties of the Ising-Glauber model on a periodic cubic lattice of linear
dimension L after a quench to zero temperature. The resulting evolution is extremely slow …

While volume violation of area law has been exhibited in several quantum spin chains, the
construction of a corresponding ground state in higher dimensions, entangled in more than …

We introduce discrete time Markov chains that preserve uniform measures on boxed plane
partitions. Elementary Markov steps change the size of the box from a× b× c to (a− 1)×(b+ …

We study a general class of log-gas ensembles on (shifted) quadratic lattices. We prove that
the corresponding empirical measures satisfy a law of large numbers and that their global …