Accurate Lower Bounds on Two-Dimensional Constraint Capacities From Corner Transfer Matrices

Upper Bounds on Two-Dimensional Constraint Capacities via Corner Transfer Matrices

We study the capacities of a family of two-dimensional constraints, containing the hard squares, non-attacking kings and read-write isolated memory models. Using an assortment of techniques from combinatorics, statistical mechanics and linear algebra, we prove upper bounds on the capacities of these models. Our starting point is Calkin and Wilf’s transfer matrix eigenvalue upper bound. We then ...

v 2 1 7 D ec 1 99 3 Infinite dimensional symmetry of corner transfer matrices

We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens many new possibilities, because the eigenstates may be described using the properties of q-vertex operators. Infinite dimensional symmetry of corner transfer ma...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Power-law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamiltonian.

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...