相关论文: The Spectral Dimension of Non-generic Branched Pol…

We show that the spectral dimension on non-generic branched polymers with positive susceptibility exponent is given by $d_s=2/(1+\gamma)$. For those models with $\gamma<0$ we find that $d_s=2$.

The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1. We show analytically that the spectral dimension of such a branched polymer…

We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…

The Gram Spectrahedron of a polynomial parametrizes its sums-of-squares representations. In this note, we determine the dimension of Gram Spectrahedra of univariate polynomials.

We define generic ensembles of infinite trees. These are limits as $N\to\infty$ of ensembles of finite trees of fixed size $N$, defined in terms of a set of branching weights. Among these ensembles are those supported on trees with vertices…

Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP…

We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short time…

We calculate the Hausdorff dimension, $d_H$, and the correlation function exponent, $\eta$, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent $\eta_0 >3$ then…

We study the average number A_n per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are…

We show random polymer is diffusive in dimensions 1 and 2 in probability in an intermediate scaling regime. The scale is $\beta= o(N^{-1/4})$ in d=1 and $\beta=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$.

We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality…

We study the multifractal properties of diffusion in the presence of an absorbing polymer and report the numerical values of the multifractal dimension spectra for the case of an absorbing self avoiding walk or random walk.

We investigate the excluded volume effects in good solvents for the isolated comb polymers having $\nu_{0}=1/4$. In particular, we investigate the change of the size exponent, $\nu$, defined by $\langle s_{N}^{2}\rangle\propto N^{2\nu}$,…

We find that 2-dimensional (2-D) critical branched polymers with no impurities conclusively belong to the same universality class as 2-D random percolation clusters, although pure critical 3-D branched polymers do not belong to the 3-D…

We obtain an essential spectral gap for $n$-dimensional convex co-compact hyperbolic manifolds with the dimension $\delta$ of the limit set close to $(n-1)/2$. The size of the gap is expressed using the additive energy of stereographic…

We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z^d viewed as a graph. We prove that for d=2 all random brushes have spectral dimension d_s=2.…

We propose a new method of the analytical computation of the spectral dimension which is based on the equivalence of the random walk and the q-state Potts model with non-zero magnetic field in the limit $q\to 0$. Calculating the critical…

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…

We report an investigation of the Snyder noncommutative spacetime and of some of its most natural generalizations, also looking at them as a powerful tool for comparing different notions of dimensionality of a quantum spacetime. It is known…

Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter…