Related papers: A simple renormalization flow for FK-percolation m…
We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.
We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in the large-$j$-limit. The vertex amplitude is deformed to include a cosmological constant term. The state…
The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level.…
We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary…
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster…
We show within the Wilson renormalization group framework how the flow equation method can be used to prove the perturbative renormalizability of a relativistic massive selfinteracting scalar field. Furthermore we prove the regularity of…
We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…
We define a hyperbolic renormalizations suitable for maps of small determinant, with uniform bounds for large periods. The techniques involve an improvement of the celebrated Palis-Takens renormalization and normal forms (fibered…
We study the renormalization flow of the Higgs potential as a function of both field amplitude and energy scale. This overcomes limitations of conventional techniques that rely, e.g., on an identification of field amplitude and RG scale, or…
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum…
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the…
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…