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arXiv:2602.02445v1 Announce Type: cross Abstract: This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees...
arXiv:2602.02446v1 Announce Type: cross Abstract: We consider a run-and-tumble particle (RTP) with stochastic resetting confined to the half line $[0,\infty)$ with a sticky boundary at...
arXiv:2602.02466v1 Announce Type: cross Abstract: The paper solves the problem of continuum limit in bosonic thermal coherent-state path integrals. For this purpose, exact discrete versions...
arXiv:1501.01889v5 Announce Type: replace Abstract: Conventional functional/path integrals used in physics are most often defined and understood, either explicitly or implicitly, as the infinite-dimensional analog...
arXiv:2006.11100v4 Announce Type: replace Abstract: Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence...
arXiv:2006.12646v4 Announce Type: replace Abstract: In this work we prove that either a sequence of axes of symmetry or a sequence of hyperplanes of symmetry...
arXiv:2009.00897v5 Announce Type: replace Abstract: Fix a word $w$ in a free group $F$ on $r$ generators. A $w$-random permutation in the symmetric group $S_N$...
arXiv:2010.00849v3 Announce Type: replace Abstract: We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ of central charge 24...
arXiv:2107.10290v4 Announce Type: replace Abstract: In this article, we prove that sequences generated by the functional calculus $(f(T)(e_n))_{n \in \mathbb{N}}$ are unitarily equivalent to function...
arXiv:2108.12935v4 Announce Type: replace Abstract: We unwind the induction implicit in the "one-step" asymptotic expansions of arXiv:1701.02417 to describe how to turn asymptotic expansions, such...
arXiv:2201.00995v3 Announce Type: replace Abstract: While information theory has been introduced to characterize the fundamental limitations of control and filtering for a few decades, the...
arXiv:2201.01234v2 Announce Type: replace Abstract: We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as...
arXiv:2201.09641v4 Announce Type: replace Abstract: We show that for the base two expansion \[ x=\sum_{i=1}^{\infty}2^{-(d_{1}(x)+d_{2}(x)+\dots+d_{i}(x))}\] with $x\in(0,1]$ and $d_{i}(x)\in\mathbb{N}$ the set $A=\{x|\lim_{i\to\infty}d_{i}(x)=\infty\}$ has Hausdorff dimension...
arXiv:2202.06587v5 Announce Type: replace Abstract: We revisit two papers which appeared in 1999: M.~Hoffmann-Ostenhof, T.~Hoffmann-Ostenhof, and N.~Nadirashvili [Ann. Global Anal. Geom. 17 (1999) 43--48] and...
arXiv:2202.13619v2 Announce Type: replace Abstract: We prove that any arithmetic locally symmetric space is homotopy equivalent to a simplicial complex where the number of simplices...
arXiv:2204.09732v2 Announce Type: replace Abstract: The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with...
arXiv:2209.00319v2 Announce Type: replace Abstract: This note contains old instead of new results about random walks on groups, which may serve as a small supplement...
arXiv:2210.07029v3 Announce Type: replace Abstract: We present three equivalent definitions of the fractional $p$-Laplacian $(-\Delta_{\mathbb{H}^{n}})^{s}_{p}$, $0
arXiv:2211.17150v2 Announce Type: replace Abstract: We say that a subset $M$ of $\mathbb R^n$ is exponentially Ramsey if there are $\epsilon>0$ and $n_0$ such that...
arXiv:2212.07973v2 Announce Type: replace Abstract: We continue the work from [8] and make a small -- but significant -- improvement to the definition of $j$-decomposable...
arXiv:2301.08312v2 Announce Type: replace Abstract: We describe an algorithm that provably computes the rational torsion subgroup of the Jacobian of a curve without relying on...
arXiv:2302.02368v4 Announce Type: replace Abstract: We rigorously derive a strain-gradient model of plasticity as a $\Gamma$-limit of continuum bodies containing finitely-many edge-dislocations (in two dimensions)....
arXiv:2303.08563v3 Announce Type: replace Abstract: We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the $\CC^\times$-fixed...
arXiv:2303.15483v3 Announce Type: replace Abstract: Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet...