A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicit…
Recent results on ergodic theory for Riemann surface laminations and foliations.
In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching.
We define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geo…
We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…
We define generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De…
This paper compares two NUTS variants and analyzes their convergence and mixing times.
The paper describes decompositions of geometric measures on Anosov homogeneous spaces.
Elliptical slice sampling converges geometrically, providing reliable sampling for Bayesian learning.
We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from overfitting or when optimizing the empirical risk is hard. For the generalization…
Estimates mixing coefficients of geometrically ergodic Markov processes from a single sample path.
The study bounds quantum eigenfunctions on complex manifolds.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
Develops Patterson-Sullivan theory for coarse cocycles.
This paper analyzes the convergence of dynamic HMC and NUTS methods.
The paper provides concentration inequalities for Markov chain variance estimators.
Given a n-dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, we …
On a compact Kähler manifold there is a canonical action of a Lie-superalgebra on the space of differential forms. It is generated by the differentials, the Lefschetz operator and the adjoints of these operators. We determine the asymptotic distribution of irreducible representations of this Lie-superalgebra on the eig…
Study invariant measures on measured laminations for subgroups of mapping class group.
Extends Masur's divergence theorem to complex tori and Kummer surfaces.
The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.
This paper studies node embeddings of networks, revealing their geometric properties.
Study on mapping class groups of non-orientable surfaces, proving some conjectures and refuting others.
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we e…
Stochastic approximation algorithms show exponential progress bounds.
Let be a Hadamard manifold, and a non-elementary discrete group of isometries of which contains a rank one isometry. We relate the ergodic theory of the geodesic flow of the quotient orbifold to the behavior of the Poincar{é} series of . Precisely, the aim of this paper is to extend the so-called…
The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a method for turning any knot into the regular planar polygon using on…
The Riemannian barycentre is one of the most widely used statistical descriptors for probability distributions on Riemannian manifolds. At present, existing algorithms are able to compute the Riemannian barycentre of a probability distribution, only if i.i.d. samples of this distribution are readily available. However,…
New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.
New MCMC methods map high-dimensional problems to spheres for better mixing.
Unfolding paths in Outer space accumulate on a simplex, not converge.
Develops geometric causal models for causal inference from dependent data.
New method for long-term sampling of complex dynamics on curved spaces.
New sampling methods improve statistical efficiency for intractable targets.
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…
Study counts ergodic measures in surface lamination strata.
In this paper, we investigate the structure of the Gardiner-Masur boundary of Teichmuller space. Indeed, we will give a geometric description of boundary comparing to the Duchin-Leininger-Rafi compactification of the space of singular flat structures. We will obtain the coincidence between the Gardiner-Masur boundary a…
Study on limits and cut-off phenomena in deep neural networks.
For a geometrically finite group Gamma of G=SO(n,1), we survey recent developments on counting and equidistribution problems for orbits of Gamma in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere countin…
The paper analyzes fixed step-size SA schemes on Riemannian manifolds.
New progress on frame flow ergodicity for nearly pinched manifolds.
Formula connects foliated simplicial volume with group cost.
In this note we show that the Riemann moduli spaces equipped with the Weil--Petersson metric are quantum ergodic for . We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.