This paper reproduces the front matter --- preface, overview and table of contents --- of a monograph by the author, submitted for publication under the title {\it Skew Linear Entropies and Kantorovich Operators: A General Aubry-Mather Theory}. The book isolates a class of non-linear operators, which we call {\it Kantorovich operators}, that are ubiquitous in analysis, probability, dynamical systems, mathematical economics and finance. We develop aspects of their ergodic theory in a way that extends classical ones involving Markov operators, free-energy transfers, or the Hopf--Lax--Oleinik semi-group. Having no adjoint, the duality between such an operator and measures is carried instead via a convex functional on {\it pairs} of probability distributions --- a source and a target --- which we call a {\it skew-linear entropy}, and which is a general form of optimal mass transport. The extensive overview reproduced here describes the resulting ergodic theory, in which minimal measures, a Mather constant, weak KAM solutions and an Aubry set are attached to an arbitrary Kantorovich operator, extending Aubry--Mather theory well beyond its origins in Hamiltonian dynamics.
We develop a machine-checked construction of non-Gaussian functional integrals using the Henstock--Kurzweil gauge integral and Chernoff product approximations. The central object is a finite family of bosonic modes with action S(phi) = (1/2) phi^T A phi + lambda * sum_i phi_i^4, where A is positive definite. We prove t...
We extend the algebro-geometric construction of bifiltered affine schemes that encode both the Higgs branch and the Macdonald index of 4d $\mathcal{N}=2$ superconformal field theories to theories with non-trivial Higgs branches. For the Argyres--Douglas theories $\mathcal{D}_p(SU(N))$, we find that a universal potentia...
We study one-dimensional Jacobi operators of divergence-gradient type on $\ell^2(\mathbb{Z}_{\geq 0})$, with coefficients generated by the doubling map, $a_n(x)=a(2^n x \mathrm{mod} 1)$. For continuous positive sampling functions, we show that the almost-sure essential spectrum is an interval containing the bottom of t...
We establish an optimal Poincar\'e inequality for real-valued symmetric observables of the complex Ginibre log-gas. Equality is attained by the real and imaginary parts of the center-of-mass observable. Equivalently, we determine the exact spectral gap of the associated overdamped Langevin dynamics, for real symmetric...
We present a direct and nonrecursive construction that maps an arbitrary planar polynomial dissipative flow $\dot{\alpha}=h(\alpha,\alpha^*)$ to an open quantum system in Gorini--Kossakowski--Sudarshan--Lindblad form. Given the homogeneous components of the classical drift, the corresponding Hamiltonian and collapse-op...
We develop the theory of the first-order dynamical systems, called the Euclidean ℰ-models, which naturally give rise in their second-order formulation to non-unitary nonlinear σ-models with real Euclidean actions. We establish the Euclidean version of Poisson-Lie T-duality, formulate sufficient conditions for Lax integ...
C. Klimčík· Journal of High Energy Physi...· 0 citations
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