Related papers: Exact renormalization groups and transportation of…
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…
The Polchinski exact renormalization group equation for a scalar field theory in arbitrary dimensions is translated, by means of a covariant Hamiltonian formalism, into a partial differential equation for an effective Hamiltonian density…
This paper explores the connection between a generalized Riesz electric energy and norms on the set of probability measures defined in terms of duality. We derive functional inequalities linking these two notions, recovering and…
An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out…
The critical exponent $\eta $ is not well accounted for in the Polchinski exact formulation of the renormalization group (RG). With a particular emphasis laid on the introduction of the critical exponent $\eta $, I re-establish (after…
The exact renormalization group is applied to the world sheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be…
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as…
In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback-Leibler…
We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
We derive the equilibrium and transport properties of metals using renormalization group equations and finite-size scaling. Particular attention is given to the well-known cases of Fermi and Luttinger liquids. An important subtlety is that…
We illustrate how the reorganization of perturbation theory at finite temperature can be economically cast in terms of the Wilson-Polchinski renormalization methods. We take as an example the old saw of the induced thermal mass of a hot…
We present a new real space renormalization-group map, on the space of probabilities, to study the renormalization of the SUSY \phi^4. In our approach we use the random walk representation on a lattice labeled by an ultrametric space. Our…
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map,…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
We derive a multiscale generalisation of the Bakry--\'Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an associated PDE well known in renormalisation theory: the Polchinski equation.…
We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $\varphi^{3}$ theory that its instability fixed points with…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincar\'{e} inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of…
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…