Related papers: Toy models for hierarchy studies
Current astrophysical models of the interstellar medium assume that small scale variation and noise can be modelled as Gaussian random fields or simple transformations thereof, such as lognormal. We use topological methods to investigate…
It is argued that the Weinberg-Salam model is the way it is because the most general self-consistent effective field theory of massive vector bosons interacting with fermions and photons at leading order coincides with the Weinberg-Salam…
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
I present a generalization of the Ehrenfest urn model that is aimed at simulating the approach to equilibrium in a dilute gas. The present model differs from the original one in two respects: 1) the two boxes have different volumes and are…
Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and $\mathbb{Z}_2$-symmetric…
We present an alternative framework to establish the neutrino mass scale from the Higgs mechanism in a minimalist approach, which does not introduce new scalar bosons or extend the symmetry group of the standard model (SM). A nonstandard…
The recent evidence for neutrino oscillations stimulate us to discuss again the problem of fermion masses and mixings in gauge theories. In the standard model, several forms for quark mass matrices are equivalent. They become ansatze within…
We investigate the building of unified models that can predict the matter-density power spectrum and the two-point correlation function from very large to small scales, being consistent with perturbation theory at low $k$ and with halo…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
The hierarchy problem of the scalar sector of the standard model is reformulated, emphasizing the role of experimental facts that may suggest the existence of a new physics large mass scale, for instance indications of the instability of…
In the original version of the theory, the driving mechanism for spontaneous symmetry breaking was identified in the pure scalar sector. However, this old idea requires a heavy Higgs particle that, after the discovery of the 125 GeV…
The standard model of particle physics is generalized so as to be furnished with a horizontal symmetry generated by an intermediary algebra between simple Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(3)$. Above a certain high energy…
The models of triangulated random surfaces embedded in (extended) Dynkin diagrams are formulated as a gauge-invariant matrix model of Weingarten type. The double scaling limit of this model is described by a collective field theory with…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
The description of electroweak physics using perturbation theory is highly successful. Though not obvious, this is due to a subtle field-theoretical effect, the Fr\"ohlich-Morchio-Strocchi mechanism, which links the physical spectrum to…
Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
In the context of gauge/gravity dualities, we calculate the scalar and tensor mass spectrum of the boundary theory defined by a special 8-scalar sigma-model in five dimensions, the background solutions of which include the 1-parameter…
We investigate the representation of hierarchical models in terms of marginals of other hierarchical models with smaller interactions. We focus on binary variables and marginals of pairwise interaction models whose hidden variables are…