Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley +1 more source
Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo +2 more
wiley +1 more source
The Linearized Inverse Boundary Value Problem in Strain Gradient Elasticity
ABSTRACT In this paper we study the linearized version of the strain gradient elasticity equation in ℝ2$$ {\mathbb{R}}^2 $$ with constant coefficients and we prove that one can determine the two Lamé coefficients λ,μ$$ \lambda, \mu $$ as well as the internal strain gradient parameter g$$ g $$, as indicated by Mindlin in his revolutionary papers in 1963–
Antonios Katsampakos +1 more
wiley +1 more source
Adaptive Sliding‐Mode Control of a Perturbed Diffusion Process With Pointwise In‐Domain Actuation
ABSTRACT A sliding mode–based adaptive control law is proposed for a class of diffusion processes featuring a spatially‐varying uncertain diffusivity and equipped with several point‐wise actuators located at the two boundaries of the spatial domain as well as in its interior.
Paul Mayr +3 more
wiley +1 more source
SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. We first compute a small time step of heat flow (middle) and then use its gradient directions to solve for a neural SDF (right). Abstract We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from ...
Samuel Weidemaier +5 more
wiley +1 more source
On initial conditions and global existence for accelerating cosmologies from string theory
We construct a solution satisfying initial conditions for accelerating cosmologies from string/M-theory. Gowdy symmetric spacetimes with a positive potential are considered.
Narita, Makoto
core +2 more sources
Measure‐valued processes for energy markets
Abstract We introduce a framework that allows to employ (non‐negative) measure‐valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how the Heath–Jarrow–Morton approach can be translated to this framework, thus guaranteeing arbitrage free ...
Christa Cuchiero +3 more
wiley +1 more source
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes ...
Aksoylu B Bernstein D Bond S Holst M +249 more
core +3 more sources
Reinforcement Learning for Jump‐Diffusions, With Financial Applications
ABSTRACT We study continuous‐time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump‐diffusion processes. We formulate an entropy‐regularized exploratory control problem with stochastic policies to capture the exploration–exploitation balance essential for RL.
Xuefeng Gao, Lingfei Li, Xun Yu Zhou
wiley +1 more source
Equilibrium Reward for Liquidity Providers in Automated Market Makers
ABSTRACT We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader–follower stochastic game, where the venue is the leader and a representative LP is the follower.
Alif Aqsha +2 more
wiley +1 more source

