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.
Study on determinants of unitary Brownian motion and their asymptotic laws.
Develops mixed quantization for graph vector bundles.
Researchers prove Weyl laws for Schrödinger operators on noncompact manifolds.
The paper studies reward concentration in MDPs, covering asymptotic and non-asymptotic settings.
Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.
In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.
Study spectral properties of sub-Riemannian Laplacians, proving quantum ergodicity and heat kernel asymptotics.
Exact asymptotic solutions found for nonlinear Hawkes processes.
New findings show neural network training loss follows a power law over time.
We prove an off-diagonal expansion for a Toeplitz operator with an indicator function.
We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase sp…
This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
The paper investigates Goodhart's law and its impact on goal alignment.
A universal learner achieves best rates for all distributions.
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
Paper approximates risk measures using SGD with Langevin dynamics.
Let be a closed Riemannian manifold carrying an effective and isometric action of a compact connected Lie group . We derive a refined remainder estimate in the stationary phase approximation of certain oscillatory integrals on with singular critical sets that were examined previously in order…
We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap …
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…
Wide CNNs outperform infinite width networks, revealing scaling laws.
Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3-5. We show how to use Friedrich et al.'s formalism to predict that…
Volatility models must be rough to match market skew.
Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black…
Law derived for neural networks with sparse connections.
We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …
We give conditions on a general stress-energy tensor T_{αβ} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay p…
The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value…
We study the heat trace for both the drifting Laplacian as well as Schrödinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term) asymptotic expansion of the heat trace for small times as well as a suitable remainder…
This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …
New scaling laws explain deep learning performance growth.
We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result…
Study on KRR with power-law data, showing better sample complexity.
Study examines risk premium convergence rates in risk sharing contracts.
Combines noncommutative geometry and spectral theory for new Weyl laws.
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual network datasets continue to grow in size, it is necessary to develop models tha…
We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace as…
Novel groups exhibit contradictory behaviors with respect to Burnside laws.
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well ap…
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…
The paper studies neural networks with wide layers and finds a deformed semicircle law.
The study uncovers universality laws for Gaussian mixtures in generalized linear models.
New insights into how depth and width affect in-context learning in deep models.
New criterion for Weyl law on Riemannian manifolds without standard assumptions.
The paper extends Weyl's law to CROSSes, showing sharpness and polynomial improvement.
Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features …
Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.