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An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).

- Luca Molinari
- 2003

The block-tridiagonal matrix structure is a common feature in Hamiltonians of models of transport. By allowing for a complex Bloch parameter in the boundary conditions, the Hamiltonian matrix and its transfer matrix are related by a spectral duality. As a consequence, I derive the distribution of the exponents of the transfer matrix in terms of the spectral… (More)

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a… (More)

- G M Cicuta, M Contedini, L Molinari
- 2008

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the n-th power of a tridiagonal matrix and the enumeration of weighted paths of n steps allows an easier combinatorial enu-meration of paths. It also seems promising for the theory… (More)

- Giovanni M Cicuta, Luca Molinari, Emilio Montaldi, Sebastiano Stramaglia
- 1995

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main diierence is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where… (More)

The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation… (More)

- Giovanni M.Cicuta, Luca Molinari
- 2001

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real… (More)

- G M Cicuta, M Contedini, L Molinari
- 1999

We study a class of tridiagonal matrix models, the " q-roots of unity " models, which includes the sign (q = 2) and the clock (q = ∞) models by Feinberg and Zee. We find that the eigenvalue densities are bounded by and have the symmetries of the regular polygon with 2q sides, in the complex plane. Furthermore the averaged traces of M k are integers that… (More)

The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given. In the appendix of their paper " Bound States in Quantum Field Theory " , Murray Gell-Mann and Francis Low… (More)

- Luca G. Molinari
- 2004

In a many body theory of fermions with two-particle interaction , I derive a variant of Hedin's equation for the vertex that contains the Hartree propagator, instead of the exact one. I count Feynman diagrams for the exact self-energy, vertex and polarization, by considering the so modified set of Hedin's equations in zero-dimensional space-time. The… (More)