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.
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
Log-ergodic model improves velocity of money prediction.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
Study shows mapping class group action is ergodic on specific representations.
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
Study shows dynamics of rank 1 orbifolds in flat surfaces.
This paper proves the following: A volume preserving vector field on a compact 3-manifold whose dual 2-form is exact can not generate uniquely ergodic dynamics unless its asymptotic linking number is zero.
This paper analyzes the convergence of dynamic HMC and NUTS methods.
The Oseledets Multiplicative Ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures at summer schools in Brazil, France, and Russia.
Study partially hyperbolic dynamics on 3-manifolds with quasi-isometric center.
We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functi…
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
Study of flows on circle bundles over translation surfaces, showing decay of correlations.
New SDE model from machine learning optimization with unique stationary distribution.
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the cond…
New method for long-term sampling of complex dynamics on curved spaces.
Continuity of earthquake flow map transfers Teichmüller dynamics results.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually makes in order to calculate ergodic stationary states, breaks down when the persiste…
We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are represented by eigenvalues of a 2x2 price operator corresponding to 'bid' and 'as…
The dynamics of holomorphic 1-forms are studied, showing ergodic foliations and connected spaces.
Method upgrades limit theorems to mixing limit theorems for dynamical systems.
In this paper we look at ergodic BSDEs in the case where the forward dynamics are given by the solution to a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck SDE with Lévy noise, taking values in a separable Hilbert space. We establish the existence of a unique bounded solution to an infinite horizon disc…
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…
Study on mean field games with singular controls and their applications.
U-turn chains improve sampling from complex distributions.
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but thei…
This paper addresses metaconsistency in Bayesian inference for metastable systems.
We study some dynamical properties of the canonical Aut(F_n)-action on the space R_n(G) of redundant representations of the free group F_n in G, where G is the group of rational points of a simple algebraic group over a local field. We show that this action is always minimal and ergodic, confirming a conjecture of A. L…
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…
Investigates spontaneous symmetry breaking in non-equilibrium systems.
New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.
The paper introduces reservoir computing models for complex systems.
We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of the action of the mapping class group of S on the deformation space. We observe…
We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit …
Study on Wasserstein distance for numerical approximations of stochastic differential equations.
We explore the dynamics of the action of the mapping class group in genus 2 on the PSL(2,R)-character variety. We prove that this action is ergodic on the connected components of Euler class 1 and -1, as it was conjectured by Goldman. In the connected component of Euler class 0 there are two invariant open subsets, on …
Study invariant measures on measured laminations for subgroups of mapping class group.
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 …
The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.
Proves CLT for Brownian paths on pinched negative curvature manifolds.
New method improves long-term forecasting of stochastic dynamical systems.
Extends Masur's divergence theorem to complex tori and Kummer surfaces.
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many exi…
The paper develops a model for sovereign debt dynamics with explicit maturity structure.
Book introduces Hofer's metric on symplectic diffeomorphisms.
This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, and connections to other areas of mathematics such as algebrai…
Study on measurable pseudo-Anosov maps on surfaces.