arXiv research

Geometric proof for averaging theorem on Riemannian manifolds.

Paper proves CLTs for Q-learning with asynchronous updates.

We use Series' Markovian coding for words in Fuchsian groups and the Bowen-Series coding of limit sets to prove an ergodic theorem for Cesaro averages of spherical averages in a Fuchsian group.

We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is distribute…

Proof of Graustein's theorem in different geometries.

Study Q-learning with averaging for reinforcement learning, proving efficient inference and error bounds.

We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers v…

New method for spot volatility estimation with reduced microstructure noise.

Theorem identifies real eigenvalues of hyperbolic Laplacian uniquely.

We give a construction to obtain canonically an ``isotropic average'' of given $C^1$-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein's submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply ``Moser's trick''. We also present an application …

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of special lagrangian and lagrangian varieties in certain homogeneous spaces.

Researchers develop a method to measure treatment effects in settings with shared states.

This paper introduces sample-averaged Q-learning for better RL performance.

We describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular) symplectic leaves are derived. We show that the construction of coupling Dirac structur…

Improves consistency of weighted averaging estimators in active learning.

Enhanced Bishop-Gromov theorem for homogeneous and inhomogeneous spaces.

The study examines how average scalar curvature influences geometric properties of Riemannian manifolds.

Given a Finsler space (M,F) on a manifold M, the averaging method associates to Finslerian geometric objects affine geometric objects} living on $M$. In particular, a Riemannian metric is associated to the fundamental tensor $g$ and an affine, torsion free connection is associated to the Chern-Rund connection. As an il…

Paper develops bounds for stochastic approximation with averaging.

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional Kähler manifold $M$ of positive and bounded holomorphic bisectional curvature, suppose its…

The standard Bonnet-Myers theorem says that if the Ricci scalar of a Riemannian manifold is bounded below by a positive number, then the manifold is compact. Moreover, a bound of its diameter is pointed out. The theorem was extended to Finsler manifolds. In this paper we prove that if a certain condition on the average…

Paper uses averaging from many particle filters to approximate posterior predictive distributions.

We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming th…

The paper computes the cohomology of cubic surfaces and their lines.

Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.

New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

Lean Copilot uses LLMs to assist theorem proving in Lean, improving efficiency and automation.

Study Edgeworth expansion for quadratic variation estimator with noise.

Paper finds optimal shapes for minimizing average lengths of billiard trajectories in specific polygons.

The study uses Ricci flow to prove flatness of certain Riemannian manifolds.

The paper derives a new theorem for predicting batches of data.

In 3-d the average projected area of a convex solid is 1/4 the surface area, as Cauchy showed in the 19th century. In general, the ratio in n dimensions may be obtained from Cauchy's surface area formula, which is in turn a special case of Kubota's theorem. However, while these latter results are well-known to those wo…

Efficient inference method for adaptive experiments with tighter confidence sequences.

The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…

The paper establishes CLTs for Markov chains and improves sampling algorithms for heavy-tailed distributions.

New method for zeroth-order stochastic gradient algorithms provides confidence intervals.

In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk patterns by optimizing an objective function, which turns out to be intimately …

In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…

Actor-Critic method achieves optimal regret for unichain MDPs.

Study proposes worst+gap measure for better DG evaluation.

The paper explores how dynamic preconditioning affects the CLT in online averaging.

Stochastic gradient descent's long-term fluctuations are described by a diffusion limit.

Study improves accuracy of risk measures using advanced algorithms.

The paper proves conditions for vanishing and estimating Betti numbers of Riemannian manifolds.

Sphere theorems proved for manifolds with specific curvature conditions.

New algorithms for collaborative learning in uncertain, decentralized environments.

In this paper, by applying a linear trace Li-Yau-Hamilton inequality for a positive (1,1)-form solution of the CR Hodge-Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete strictly pseudocovex CR manifold with nonnegative pseudohermitian bisectional c…