Related papers: High-gradient operators in the N-vector model
The purpose of this Note is to highlight the spectral instability of some non-selfadjoint differential operators, by studying the growth rate of the norms of the spectral projections $\Pi_n$ associated with their eigenvalues. More…
Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence…
We obtain the operator product expansion of the self-energy in the O(N) non-linear $\sigma$-model to all orders in the coupling and the large momentum, and to next-to-leading order in 1/N. In the light of this result we discuss recent…
We consider the class of higher derivative $3d$ vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For $n$-th order theory of this type, we provide a general receipt for constructing…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…
$V$ denotes arbitrary bounded bijection on Hilbert space $H$. We try to describe the sets of $V$-stable vectors, i.e. the set of elements $x$ of $H$ such that the sequence $\|V^N x\| (N=1,2,...)$ is bounded (we also consider some other…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and…
Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis. Five years ago, it was shown that if finitely many firmly nonexpansive operators are all asymptotically regular…
We review some of the problems associated with deriving field theoretic results from nonsupersymmetric AdS, focusing on how to control the behavior of the field theory along the flat directions. We discuss an example in which the origin of…
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…
Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with $p$-growth. This work is dedicated to a quantitative…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
Supergravity theory in $2+\epsilon$ dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…