相关论文: The $\epsilon$ expansion and Universality in three…
We study the behavior of the random walk on the infinite cluster of independent long range percolation in dimensions $d=1,2$, where $x$ and $y$ a re connected with probability $\sim\beta/\|x-y\|^{-s}$. We show that when $d<s<2d$ the walk is…
Nourdin et al. [9] established the following universality result: if a sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal random variables converges in distribution to a normal, then the convergence also holds…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…
We study universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length $L$ and a persistence length $\ell_p$ in two dimensions (2D) and in three dimensions (3D) in the…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
This paper is part of a program by Feldman, Trubowitz and ourselves to construct a mathematically rigorous version of the BCS mechanism for superconductivity. In previous papers the renormalization group around the Fermi surface was defined…
Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension $-1$ exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of…
Non-Hermitian random matrices have been utilized in such diverse fields as dissipative and stochastic processes, mesoscopic physics, nuclear physics, and neural networks. However, the only known universal level-spacing statistics is that of…
We investigate the critical properties of the Lee-Yang model in less than six spacetime dimensions using truncations of the functional renormalization group flow. We give estimates for the critical exponents, study the dependence on the…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
We show that the scaling limit exists and is invariant to dilations and rotations. We give some tools that might be useful to show universality.
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show…
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
Annihilation processes, where the reacting particles are influenced by some external advective field, are one of the simplest examples of nonlinear statistical systems. This type of processes can be observed in miscellaneous chemical,…
We have investigated both site and bond percolation on two dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked…