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We study the conjugation action of orthogonal matrices on symmetric random matrices. Given a fixed orthogonal matrix over an algebraic number field and a random matrix with entries sufficiently uniform in the ring of integers, we wonder…
One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the…
Some years ago it was shown that the cosmological constant may be reduced by thermal production of membranes that, after nucleation, collapse into a black hole. The probability of the process was calculated in the leading semiclassical…
Finite systems in confining potentials are known to undergo structural transitions similar to phase transitions. However, these systems are inhomogeneous, and their "melting" point may depend on the position in the trap and vary with the…
We study random sequential adsorption (RSA) of a class of solids that can be obtained from a cube by specific cutting of its vertices, in order to find out how the transition from tetrahedral to octahedral symmetry affects the densities of…
By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesin's entropy formula and SRB measures of a finitely generated random…
A toy model of particles packings is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the…
We derive explicit expressions for the volume elements of both the minimal and maximal monotone metrics over the (n^{2} - 1)-dimensional convex set of n x n density matrices for the cases n = 3 and 4. We make further progress for the…
Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we…
We consider asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a…
Spectrahedra are affine-linear sections of the cone $\mathcal{P}_n$ of positive semidefinite symmetric $n\times n$-matrices. We consider random spectrahedra that are obtained by intersecting~$\mathcal{P}_n$ with the affine-linear space…
Using three-dimensional general relativistic magnetohydrodynamic simulations with electron and proton thermodynamics and an electron cooling function, we probe the inner radial and vertical structure of weakly magnetized geometrically thin…
The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
We study the effect of the choice of embedding geometry on the entropy of random geometric graph ensembles with soft connection functions. First we show that when the connection range is small, the entropy is dependent only on the dimension…
Framing triangulations of unit flow polytopes have received a great deal of recent study with rich connections to various generalizations of Catalan and Cambrian combinatorics as well as volume and h*-polynomial formulas. This story has…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of $\mathbb{R}^3$ can be completely softened. A weaker form of this statement, for polyhedral space tilings, was conjectured by Domokos,…
We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically…
In 1900, as a part of his 18th problem, Hilbert proposed the question to determine the densest congruent (or translative) packings of a given solid, such as the unit ball or the regular tetrahedron of unit edges. Up to now, our knowledge…