arXiv research

Unified theory of measure-preserving diffusions on manifolds.

The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.

The study shows finite measure-preserving isometry groups for certain metric measure spaces.

Study shows infinite-dimensional third bounded cohomology for non-orientable surfaces.

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…

We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular, we derive conditions for the existence of the minimal martingale measure. We al…

Study curvatures of diffeomorphisms on non-orientable surfaces.

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.

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…

Characterizes measures preserving compound mixed renewal process properties.

Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping cl…

The paper explores arbitrage opportunities in derivative markets under specific conditions.

For a commodity spot price dynamics given by an Ornstein-Uhlenbeck process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium i…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can b…

We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space …

We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splitting theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can pe…

New expanders found using origami surfaces with spectral gap.

Suppose M is a noncompact connected 2-manifold and m is a good Radon measure of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the group of homeomorphisms of M equipped with the compact-open topology and let H(M; m)_0 denote the identity component of the subgroup consisting of m-preserving homeomo…

New copula models capture volatility and directionality in financial time series.

New framework uses simplicial and categorical methods to detect market inconsistencies.

Handlebody groups are rigid under measure equivalence.

We give necessary and sufficient conditions that show that both the group of isometries and the group of measure-preserving isometries are Lie groups for a large class of metric measure spaces. In addition we study, among other examples, whether spaces having a generalized lower Ricci curvature bound fulfill these requ…

For a positive integer $n\ge 3$, the collection of $n$-sided polygons embedded in $3$-space defines the space of geometric knots. We will consider the subspace of equilateral knots, consisting of embedded $n$-sided polygons with unit length edges. Paths in this space determine isotopies of polygons, so path-components …

Study graph products of groups, classifying them up to measure equivalence and rigidity.

Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action of G satisfies a nonwandering hypothesis, then the action has a global fixed po…

We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry. It happened that the generic Polish spaces in this sense of this universum is so called Urysohn spaces defined by P.S.Urysohn in 20-th, and generic metric triple (= metric space with…

Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving homeomorphisms of M equipped with the compact-open topology and H_E(M; m) denote the subgroup consisting of all h in H(M; m) which fix the ends of M. Each h in H_E(M; m) mov…

MixFlows uses a mixture of flows for efficient variational inference.

In this note, we embed the set of all Fricke characters of a free group F -- the set of all characters of representations of F into SL(2,C) -- as an irreducible affine variety V in complex affine space of dimension 2^n-1. Using the Horowitz generating set as the indeterminates, we show that the ideal I of all polynomia…

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is significantly influenced by the choice of the proposal. Recently Ha…

Automates learning of multivariate diffusions for generative models.

Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.

Diffusion-GAN uses diffusion to improve GAN training stability and realism.

The paper defines and proves non-triviality of volume and Euler classes in bounded cohomology of transformation groups.

Study shows how heat leaks from material sets in low diffusivity scenarios.

New blurring diffusion models bridge heat dissipation and denoising.

Study mass transport in low-diffusivity using Lagrangian coordinates.

New method tackles video inverse problems using image diffusion models.

Diffusion models generate new samples with active guidance, but theory is limited.

We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of $2π$, determines a holonomy representation …

Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.

PaGoDA reduces diffusion model training costs by 64x.

Study shows diffused interface flows to single diffused balls over time.

Latent diffusion improves robustness in missing data imputation.

The paper examines smoothness in diffusion algebra.

DMPS uses diffusion maps and LAWGD for efficient generative modeling.

Develops a new model for pricing without arbitrage opportunities.