arXiv preprints from January 1, 2026 through September 23, 2026 — 23:03:44 EST
In this paper, we establish the boundedness of the bilinear Bochner-Riesz means $\mathcal{B}^α_R$ on the complex sphere $\mathbb{S}$. More precisely, we prove that $\mathcal{B}^α_R$ is bounded from $L^{p_1}(\mathbb{S}) \times L^{p_2}(\mathbb{S}) \to L^p(\mathbb{S})$ where $1/p_1+1/p_2=1/p$ and $1\leq p_1, p_2 \leq \infty$, for an...
We prove mode stability for the massless scalar wave equation on Kerr-de Sitter black hole spacetimes in the full subextremal range. In combination with recent work by Petersen-Vasy, this proves, unconditionally, that sufficiently regular solutions of the scalar wave equation decay exponentially fast to constants.
Böhm metrics on $S^{k+1}\times S^l$ and $S^{k+l+1}$ ($k,l\geqslant 2$, $k+l\leqslant 8$) occur in sequences of Einstein metrics that converge to a cone. We prove that, along such a sequence, the number of negative eigenvalues of the Lichnerowicz Laplacian acting on transverse-traceless tensors tends to infinity: these metrics become...
The huge amount of literature about the divergence equation in bounded Lipschitz domains of $\R^n$ ($n\ge2$) is fairly disconnected and even apparently simple problems remain unsolved. We go several steps further in the knowledge of this equation and of some related inequalities. We prove that among its infinitely many solutions there...
We study steady solutions to the two-dimensional incompressible Euler equations in an infinite channel, whose far-field limits are uniformly non-stagnant shear flows. In the smooth category,for a broad class of prescribed far-field shear profiles, non-shear steady states exist via the construction of two-dimensional solutions of the...
For a finite associative unital ring $R$, the null ideal of $R$ is the collection of polynomials with coefficients from $R$ that send each element of $R$ to zero under evaluation. It was conjectured that the null ideal of $R$ is always a two-sided ideal of its overlying polynomial ring. The conjecture was proved to be false with the...
Randomization testing with permutations is a very common nonparametric approach to hypothesis testing. However, randomization testing can be done with other group transformations including random rotations. In this work, we consider the problem of invariance in quadratic form statistics under a unified framework with closed form...
Driver behavior is heterogeneous, context-dependent, and changes over time, and these properties shape the traffic phenomena we observe. Most models, however, fix in advance which behavioral variables interact and how. Behavior outside that form is absorbed as noise, while models flexible enough to capture it tend to lose...
An intuitive method for dimensionality reduction is proposed, which is highly effective for finding interesting projections of multivariate data. Following similar intuitive motivation to a number of existing techniques, the proposed method is based on enhancing the nearest neighbour relationships in the data. The proposed projection...
This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to...
Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central. Existing variants rely on fixed bases such as splines, polynomials, or Fourier features, which impose a function-space geometry before data are observed. We...
Epidemic models often pool air travel, commuting, and other mobility layers into a single weighted network. Pooling keeps the total imported infections into a region but discards the transport mode and route that delivered them, the information a mode-specific intervention needs. We make this precise for directed multilayer flows with...
A key result in statistics is the data processing inequality, originally proved by Blackwell (1951) and later refined by DeGroot (1962) in terms of statistical uncertainty. It states that the Bayes risk of a statistical experiment obtained by stochastically modifying another experiment cannot be lower than the Bayes risk of the...
We address the simultaneous prediction of multiple high-dimensional physical fields governed by linear equality constraints, a setting that arises in many real-world applications in physics machine learning. Gaussian process (GP) regression is a widely used surrogate modeling approach due to its effectiveness in small-sample regimes...
Exact Bayes prediction enjoys fast predictive regret guarantees, but exact posterior updating or representation may be too costly for online use. We study when these statistical guarantees are preserved by computational approximations. We show that the cumulative price of posterior approximation can be governed by the interaction...
The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet the rich dynamics of its time-dependent joint distribution over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to systematically characterize the nonequilibrium...
Spatiotemporal ARCH models capture temporal volatility persistence and cross-sectional dependence but typically require a predefined spatial weight matrix. This is restrictive in financial markets, where the dependence network is rarely known. We develop a LASSO-penalised quasi-maximum likelihood estimator that jointly learns a sparse...
Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory. This mismatch creates a fundamental certification problem: fixed-time guarantees do not generally remain valid at...
Random feature methods provide a scalable approximation to kernel ridge regression (KRR), but the regularization parameter that yields the oracle learning rate depends on unknown smoothness and capacity parameters. In this work, we propose a neighboring early-stopping rule for adaptive regularization in KRR with random features...
Functional data analysis is an important statistical field that treats data as random functions. In practice, the random functions are often not fully observed but instead measured at discrete times. While simpler problems, such as mean and covariance estimation, have been widely studied for discretely observed data, optimal...
We establish non-asymptotic Berry--Esseen bounds and bootstrap approximations for the Hilbert-space norm of nondegenerate $U$-statistics. Our triangular-array framework allows the kernel to take values in a separable Hilbert space $H_n$ that may vary with the sample size, thereby covering both infinite-dimensional spaces and Euclidean...
Bayesian methods are essential in modern data analysis in ecology and evolutionary biology. They provide a flexible framework for modeling complex data-generating processes, while quantifying uncertainty based on the classical subjective interpretation of probability. However, Bayesian inference may provide misleading measures of...
We propose an omnibus nonparametric test for structural changes in the multivariate volatility matrix. The test aggregates bounded generalized quantile scores over a range of quantile levels and has a weighted leave-$q$-out $U$-statistic representation. Deleting nearby index pairs renders the centering effect induced by serial...
Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose...
Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon, as needed in applications...