Related papers: Functional Renormalization Group Approach for Sign…
Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address…
The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
Signal detection is one of the main challenges of data science. As it often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques aimed at extracting the relevant degrees of freedom…
Signal detection in high dimensions is a critical challenge in data science. While standard methods based on random matrix theory provide sharp detection thresholds for finite-rank perturbations, such as the known Baik-Ben Arous-P\'ech\'e…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…