arXiv preprints from January 1, 2026 through September 8, 2026 — 15:31:55 EST
The randomly pivoted Cholesky algorithm is one of the leading methods for computing a low-rank approximation to a large positive-semidefinite matrix. However, while it consistently achieves accuracy comparable to or better than competing methods of its type in experiments, its theoretical analysis lags somewhat behind other methods....
We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously, so that the contemporaneous controls used by difference-in-differences and synthetic control are unavailable and the counterfactual must be extrapolated from a unit's own pre-treatment history. We establish identification...
In many applications, from government to ecology, integrating data from diverse and noisy sources is critical for downstream inference. However, a unique identifier to link records cleanly from the same entity may not exist. Entity resolution (also referred to as de-duplication or record linkage) merges such databases to identify...
Neural survival models are increasingly asked to support counterfactual claims---how much a treatment would change survival in a population---rather than only prognostic risk scores. Answering such questions from observational data requires valid inference for treatment-specific survival contrasts under confounding and...
Deep hedging is a data-driven approach to learn hedging strategies. It relies on synthetic price paths generator, as real market data is often limited for training. Existing approaches primarily evaluate such generators based on realism, i.e., how well they capture statistical properties of real markets, but the relationship between...
Tests of conditional mean independence can lose power when departures are confined to a bounded part of a multivariate predictor space and the relevant spatial scale is unknown. We propose a Multiscale Ball Conditional Mean Independence (MBCMI) test that aggregates support-weighted local mean contrasts in an outcome variable across...
The Marketron model of \cite{HalperinItkin2025Mark} and its option pricing extension in \cite{HalperinItkinMarketron2} suffer from structural non-identifiability: an eighteen-parameter space traps solvers in suboptimal local minima and renders economic quantities unmeasurable. By removing exact scaling gauges and sign symmetries,...
We study finitely generated maximal right ideals of the Banach algebra $\mathcal{B}(E)$ of bounded operators on a complex Banach space $E$. Every maximal right ideal is either fixed by a non-zero functional or contains the ideal of finite-rank operators; when $E$ is infinite-dimensional, each non-fixed maximal right ideal in fact...
We consider a competition between two independent random walks on a cycle of length $N$. Each vertex is claimed by the walker that visits it first, and remains claimed thereafter. We prove that if the initial distance between the walkers is $d$, then the expected number of edges whose endpoints are claimed by different walkers is of...
The retrieval dynamics of a modern Hopfield network is the gradient flow of a log-sum-exp energy, while the attention update is its exact difference-of-convex minimization step. We study which time discretizations preserve not only energy decay and equilibria but also basins of attraction. We introduce energy cells, connected...
Hyperelliptic theta divisors, and more generally, Brill-Noether loci, are shown to be locally catalecticant determinantal varieties. This has many consequences for their local and global structure.
We solve the problem of explicitly constructing a continuous function whose unique maximizing measure for the doubling map is Lebesgue measure. More generally, given a nontrivial compact metrizable abelian group and a continuous surjective endomorphism for which normalised Haar measure is ergodic, we explicitly construct a continuous...
A Banach space $X$ has the SHAI property if, for every non-zero Banach space $Y$, every surjective algebra homomorphism from the algebra $\mathcal{L}(X)$ of bounded linear operators on $X$ onto $\mathcal{L}(Y)$ is injective. In this work, we prove that the Bourgain-Rosenthal-Schechtman spaces have the SHAI property, thereby answering...
Motivated by refinements of Kunz's theorem involving the growth of Betti numbers, we study Betti and Bass numbers associated to the relative Frobenius. Under appropriate hypotheses on a local ring homomorphism $\varphi \colon R \to S$, we obtain bounds on the growth of the Betti and Bass numbers of relative Frobenius pushforwards of...
Cluster varieties contain the union of cluster tori and the points not in this union are called $\textit{deep points}$, and the locus of these points is called the $\textit{deep locus}$. In arXiv:2402.16970, a description of this locus is conjectured for locally acyclic cluster algebras, in particular, stating that this should be the...
Consider a free product $(M,\varphi)= (M_1,\varphi_1)* (M_2,\varphi_2)$ of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral gap results for free product subalgebras and the centralizer subalgebra of the free product state. In particular, it is shown that, under...
We give a self-contained finite-precision analysis of the symmetric Lanczos algorithm without reorthogonalization. In particular, we derive the perturbed three-term recurrence, Paige's loss-of-orthogonality identity, containment of all computed Ritz values, and localization of stabilized Ritz values. We then prove a Greenbaum-type...
The recent work of Sarkar and Zhang (2025) introduced Positive Tail Dependence Under the Null (PTDN) and developed Generalized Shifted Benjamini-Hochberg (BH) procedures for two-sided Gaussian $z$- and $t$-testing under known covariance structures. This paper develops further consequences of that framework. First, we derive explicit...
We prove that every prime Fano threefold of genus $\geq 7$ in positive characteristic is a linear section of a Mukai variety.
Let $X$ be a prime Fano threefold of genus $g\geq 8$ in positive characteristic. For every nontrivial decomposition $g =rs$, we prove that there exists a unique Mukai bundle on $X$ of type $(r, s)$. To this end, we show that every smooth hyperplane section of $X$ is Brill-Noether general.
In this paper we prove the equality of the dimensions IndX and dimX for any stratifiable spaces. As a consequence, we obtain the equality of the dimensions IndX, indX and dimX for stratifiable spaces with a countable network. It has been proven that every stratifiable space is an S-space (possesses an S-network).
For each $s>0$, we consider a random Dirichlet series $X(s)=\sum_{k\geq 1}k^{-1/2-s}a_kη_k$, where $η_1$, $η_2,\ldots$ are independent and identically distributed random variables with mean zero and finite positive variance, and $(a_k)_{k\geq 1}$ is a deterministic sequence of real numbers satisfying $\sum_{k\geq...
We study \emph{$T$-Robinson spaces}, a tree-based generalization of Robinson spaces in which every path of a compatible tree induces a Robinson subspace. This framework extends the classical notion of Robinsonian representations from linear orderings to tree structures, allowing the modeling of hierarchical and branching data. We...
When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we...
A first-principles and device-level study of the quasi-two-dimensional transition-metal chalcogenide Mo$_2$SeTe$_3$ is performed. The material is found to be a weak topological semiconductor with a finite bulk band gap and symmetry-protected Dirac surface states, indicating strong potential for next-generation low-power quantum...