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Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the…
We study the statistics of the recurrence times between earthquakes above a certain magnitude M$ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $\tau_0$. As a…
We study spherically-symmetric solutions to a modified Einstein-Hilbert action with Renormalization Group scale-dependent couplings, inspired by Weinberg's Asymptotic Safety scenario for Quantum Gravity. The Renormalization Group scale is…
We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the…
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show,…
In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
We illustrate the importance of mass scales and their relation in the specific case of the linear sigma model within the context of its one loop Ward identities. In the calculation it becomes apparent the delicate and essential connection…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
We study numerically a two-dimensional version of the Burrige-Knopoff model. We calculate spatial and temporal correlation functions and compare their behavior with the results found for the one-dimensional model. The Gutenberg-Richter law…
In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of 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 study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…
The empirical Bath's law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair distribution related to earthquake correlations is presented. The single-event distribution of dynamically correlated…
It is shown that the correlation integrals (invariants) play an important, and at certain conditions a dominant, role in helical isotropic homogeneous turbulence both in the inertial and near-dissipation ranges. Results of direct numerical…