Related papers: An Improved Mean Field Approximation on the Worlds…
This paper is concerned with the global stability of the plane wave solutions to the relativistic string equation with non-small perturbations. Under certain decay assumptions on the plane wave, we conclude that the perturbed system admits…
We construct analytic solutions of open superstring field theory for any exactly marginal deformation in any boundary superconformal field theory when properly renormalized operator products of the marginal operator are given. Our…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered with…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…
One proposal for deriving effective cosmological models from theories of quantum gravity is to view the former as a mean-field (hydrodynamic) description of the latter, which describes a universe formed by a 'condensate' of quanta of…
We use the theory of arithmetic quotients of the Bruhat-Tits tree developed by Serre and others to obtain Dirichlet-style theorems for Diophantine approximation on global function fields. This approach allows us to find sharp values for the…
The mean field approximation becomes applicable when entanglement is sufficiently weak. We explore a nonlinear term that can be added to the Schr\"{o}dinger equation without violating unitarity of the time evolution. We find that the added…
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a…
Recently, a number of authors have challenged the conventional assumption that the string scale, Planck mass, and unification scale are roughly comparable. It has been suggested that the string scale could be as low as a TeV. The greatest…
In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in…
We derive a class of solutions to the string sigma-model equations for the closed bosonic string. The tachyon field is taken to form a constant condensate and the beta-function equations at one-loop level are solved for the evolution of the…
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…
In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of…
Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the $\phi^6-$field theory. Further, it is shown that the exact solutions of the Lienard equation are also the…
The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation of Gambini and Trias, and Rovelli and Smolin) is formulated as a weighted sum over worldsheets interpolating between…
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate…
Recent results on the effective non-local dynamics of the tachyon mode of open string field theory (OSFT) show that approximate solutions can be constructed which obey the diffusion equation. We argue that this structure is inherited from…
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…
We have constructed the mean-field trivial solution of the $\varphi^4$ theory $O(N)$ model in four dimensions in two previous papers using the flow equations of the renormalization group. Here we establish a relation between the trivial…
We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $\mathcal{M}_3 \times \mathrm{S}^3 \times…