arXiv research

The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.

New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.

The paper connects geodesic flows, hyperbolic geodesics, and stable ergodicity.

Strong stability of ergodic iterations proven without ergodic driving sequence.

We show that non-elliptic prime 3-manifolds satisfy integral approximation for the simplicial volume, i.e., that their simplicial volume equals the stable integral simplicial volume. The proof makes use of integral foliated simplicial volume and tools from ergodic theory.

We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.

This paper addresses metaconsistency in Bayesian inference for metastable systems.

The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.

Extends Kanai's result to higher dimensions for negatively curved manifolds.

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of …

Approximates measures on curved spaces using Dirac measures.

Study counts ergodic measures in surface lamination strata.

Study on measurable pseudo-Anosov maps on surfaces.

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…

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action of the fundamental group on a probability space. We show that integral foliated s…

New progress on frame flow ergodicity for nearly pinched manifolds.

Recent results on ergodic theory for Riemann surface laminations and foliations.

Formula connects foliated simplicial volume with group cost.

In this note we show that the Riemann moduli spaces $M_{g, n}$ equipped with the Weil--Petersson metric are quantum ergodic for $3g+n \geq 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quan…

The paper studies the ergodicity of frame flow on even-dimensional manifolds.

Non-ergodic measures found in horocycle flow on Abelian differentials.

Log-ergodic model improves velocity of money prediction.

'Ergodicity economics' is criticized as pseudoscience.

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…

The study shows that ergodic measures are not generic on non-positively curved manifolds.

We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law involving the flat systole of a Teichmüller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodi…

We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…

The paper studies ergodicity of flows on subspaces, generalizing earlier work.

A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant). Ergodic translations on tori are classical examples of DUE diffeomorphisms. In this ar…

A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (u…

The study proves conditions for rigidity of Kleinian groups using measure theory and ergodic theory.

The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.

This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.

Study shows non-wandering, partially hyperbolic systems are ergodic.

We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids with a transversal measure into smooth manifolds, generalizing Ruelle…

Study shows mapping class group action is ergodic on specific representations.

The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question …

We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergod…

We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of αin [0, 1) so that T composed with R_α is uniquely ergodic, where R_α is rotation by α.

SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.

In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a…

We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …

Classifies 3D partially hyperbolic systems, proving ergodicity.

Paper shows ergodicity and irreducibility of mapping class group boundary representation.

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…

New rule universally consistent for online learning with non-ergodic data.