arXiv research

Labels define the effective timescale for learning from short observations.

Study proves fluid limits of fragmented limit-order markets.

We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometr…

The paper models and analyzes the dynamics of a limit order book using Hawkes processes.

Method upgrades limit theorems to mixing limit theorems for dynamical systems.

New examples show strong Kato limits can be branching and not satisfy known conditions.

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the beh…

The large-N limit of Segal-Bargmann transform on spheres is studied.

A limit group is the limit of a sequence of conjugates of the diagonal Cartan subgroup, C, of SL(3,R). We show C has 5 possible limit groups, up to conjugacy. Each limit group is determined by an equivalence class of nonstandard triangle, and we give a criterion for a sequence of conjugates of C to converge to each of …

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limi…

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…

Two price regimes identified in limit order books: close and far from quotes.

Paper studies Hausdorff dimension of limit sets for Kleinian groups.

Study compares price limit and circuit breaker effects in stock markets.

Study describes limits of non-collapsing K3 surfaces using algebraic data.

Finite genus embedded minimal surfaces have limited limit ends.

Study of conformal limits in Nakajima quiver varieties.

Study on the limits of projective special real manifolds and their symmetries.

Find limiting sets for digital cones and suspensions.

Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of pri…

Easy condition for local k-connectedness in inverse limits of polyhedra.

New framework for understanding infinite-width neural networks.

We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under logarithmic loss, we show that in the finite space setting, when it is possible to…

Study examines infinite limits of transformer dynamics, identifying key parameterizations.

Study the topology of Ricci limit spaces using Gromov-Hausdorff limits.

Study smooth convergence of metric flows from $\mathbb{F}$-limits.

Study projective and direct limits of Banach structures with connections to $G$-structures.

This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2π. We show that these are in a natrual way projective algebraic var…

The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price acc…

Troels Jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in the algebraic limit. We prove that this conjecture holds in 'most' cases. In particular, we show that it holds when the domain of discontinui…

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.

Study continuity of limit sets in symmetric spaces.

Study shows spectral gaps limit points on surfaces.

The optimistic limit is the mathematical formulation of the classical limit which is a physical method to expect the actual limit by using saddle point method of certain potential function. The original optimistic limit of the Kashaev invariant was formulated by Yokota, and a modified formulation was suggested by the a…

Integrability criterion for projective limits of Banach distributions on Fréchet manifolds.

This article gives solutions to the exercises in Bestvina and Feighn's paper on Sela's work on limit groups. We prove that all constructible limit groups are limit groups and give an account of the shortening argument of Rips and Sela.

Study finds limit points of bass notes on hyperbolic surfaces.

Study local limits of subgroups in $SL_3(\mathbb{R})$.

In this article, we study the relationship between the weak limit of a sequence of integral currents in a metric space and the possible Hausdorff limit of the sequence of supports. Due to cancellation, the weak limit is in general supported in a strict subset of the Hausdorff limit. We exhibit sufficient conditions in …

Tests if market noise is explained by limit order book variables.

Study shows Julia sets and gasket limit sets are quasiconformally different.

Characterizes extreme points in polygon limit sets.

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

Study proves uniqueness of asymptotic limits for specific manifolds.

Proves a central limit theorem for neural networks with hidden layers.

Paper introduces new Hawkes processes to model price changes in limit order books.

Ancient ovals are key blowup limits in 3D Ricci flow near singularities.