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Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
Recent seminal work at the intersection of deep neural networks practice and random matrix theory has linked the convergence speed and robustness of these networks with the combination of random weight initialization and nonlinear…
We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a…
We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW universe. Its computation is based on the extension of the adiabatic regularization method…
In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained…
We calculate two-point energy level correlation function in weakly disorderd metallic grain with taking account of localization corrections to the universal random matrix result. Using supersymmetric nonlinear sigma model and exactly…
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper…
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…
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…
It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it…
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal…
We consider the self-force on a charged particle moving in a curved spacetime with a background electromagnetic field, extending previous studies to situations in which gravitational and electromagnetic perturbations are comparable. The…
In linearized quantum gravity, a shift of the average energy-momentum can be compensated by a shift of the average gravitational field. This allows a renormalization scheme that naturally removes the contribution of quantum vacuum…
Functional renormalization yields a simple unified description of bosons at zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields. We concentrate on nonrelativistic bosons and an action with a linear time derivative.…
Renormalization Group Equations (RGEs) are indispensable tool to know the behavior of physical parameters at different energy scales. They are also extremely crucial if we want to extend our known Standard Model gauge group by some extra…