Related papers: The Gradient flow equation of Rabinowitz action fu…

We study both the local and global existence of a gradient flow of the Sinai-Ruelle-Bowen entropy functional on a Hilbert manifold of expanding maps of a circle equipped with a Sobolev norm in the tangent space of the manifold. We show…

An elementary analytical fluid flow is composed by a geometric domain, a list of analytical constraints and by the function which depends on the physical properties, as Reynolds number, of the considered fluid. For this object, notions of…

R. Thom's gradient conjecture states that if a gradient flow of an analytic function converges to a limit, it does so along a unique limiting direction. In this paper, we extend and settle this conjecture in the context of infinite…

We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…

We study the $L^2$-gradient flows, $\partial_t u-\mathrm{div}(\mathrm{D}f(x,\mathbb{A}u))=0$, of functionals of the type $\int_{\Omega}f(x,\mathbb{A}u)\,\mathrm{d}x$, where $f$ is a convex function of linear growth and $\mathbb{A}$ is some…

We study the perturbative behavior of the Yang-Mills gradient flow in the Schr\"odinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the…

In the frame of the Boltzmann equation, wall-bounded flows of rarefied gases require the implementation of boundary conditions at the kinetic level. Such boundary conditions induce a discontinuity in the distribution function with respect…

We study the $L^2$-gradient flow of functionals $\mathcal F$ depending on the eigenvalues of Schr\"odinger potentials $V$ for a wide class of differential operators associated to closed, symmetric, and coercive bilinear forms, including the…

In the case of a compact real analytic symplectic manifold M we describe an approach to the complexification of Hamiltonian flows [Se, Do1, Th1] and corresponding geodesics on the space of Kahler metrics. In this approach, motivated by…

Given any continuous, lower bounded and $\kappa$-convex function $V$ on a metric measure space $(X,d,m)$ which is infinitesimally Hilbertian and satisfies some synthetic lower bound for the Ricci curvature in the sense of…

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be…

We introduce a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows with modest decay using limits of conjugate heat flows. This functional satisfies a steady Ricci breather-type rigidity and provides an…

Symanzik effective actions, conjectured to describe lattice artifacts, are determined for a class of lattice regularizations of the non-linear O(N) sigma model in two dimensions in the leading order of the 1/N-expansion. The class of…

In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG $\beta$ function, an alternative…

Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this…

In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…

This paper deals with the boundary behavior of functions in the de Branges--Rovnyak spaces. First, we give a criterion for the existence of radial limits for the derivatives of functions in the de Branges--Rovnyak spaces. This criterion…

We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof…

For a given pseudo-Anosov homeomorphism $\varphi$ of a closed surface $S$, the action of $\varphi$ on the Teichm\"uller space $\mathcal T(S)$ preserves the Weil-Petersson symplectic form. We give explicit formulae for two invariant…

The metric and potential associated with the gradient property of renormalisation group flow in multiscalar models in $d=4-\varepsilon$ dimensions are studied. The metric is identified with the Zamolodchikov metric of nearly marginal…