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Andres Larrain-Hubach

Publications and source records attributed to Andres Larrain-Hubach.

8 recordsLinked to original sources
arXiv2023

A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands

In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences Markovian inter-demand and service intervals with random service interruptions and instantaneous replenishments. A recently developed criterion for the ergodicity of a class of discrete-time level-dependent-quasi-birth-and-death (LDQBD) processes with convergent transition matrix rows is applied to the jump chain of the process in order to elicit a closed-form traffic-intensity formula. An analytic solution for the steady-state average minimum cost is provided.

math.PR↗
arXiv2022

Some Modifications of Getzler's Grading technique

This paper reviews the grading technique developed by Getzler to prove the local index theorem and shows how to adapt it to compute the leading terms of asymptotic expansions of traces of heat kernels in two other situations.

math.DG↗
arXiv2019

Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem

We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.

math.DG↗
arXiv2018

Sobolev Maps into Compact Lie Groups and Curvature

These are notes on seminal work of Freed, and subsequent developments, on the curvature properties of (Sobolev Lie) groups of maps from a Riemannian manifold into a compact Lie group. We are mainly interested in critical cases which are relevant to quantum field theory. For example Freed showed that, in a necessarily qualified sense, the quotient space $W^{1/2}(S^1,K)/K$ is a (positive constant) Einstein `manifold' with respect to the essentially unique PSU(1,1) invariant metric, where $W^{s}$ denotes maps of $L^2$ Sobolev order s. In a similarly qualified sense, and in addition making use of the Dixmier trace/Wodzicki residue, we show that for a Riemann surface Sigma, $W^1(Σ,K)/K$ is a (positive constant) Einstein `manifold' with respect to the essentially unique conformally invariant metric. As in the one dimensional case, invariance implies Einstein, but the sign of the Ricci curvature has to be computed. Because of the qualifications involved in these statements, in practice it is necessary to consider curvature for $W^s(Σ,K)$ for s above the critical exponent, and limits. The formula we obtain is surprisingly simple.

math.DG↗
arXiv2015

Equivariant, string and leading order characteristic classes associated to fibrations

We construct equivariant, string and leading order characteristic classes and Chern-Simons classes for certain infinite rank bundles associated to fibrations occurring in loop spaces, Gromov-Witten theory and gauge theory. Results include a restatement of the S^1 index theorem using equivariant classes on the tangent bundle to loop space; the expression of some GW invariants in terms of string and leading order classes for infinite rank bundles over moduli spaces of pseudoholomorphic curves for semipositive symplectic manifolds; the identification of the real cohomology of a loop group with certain string and leading order classes; the identification of Donaldson's nu-class for 4-manifolds with a leading order class for the fibration of irreducible connections A over the quotient A/G by the gauge group.

math-ph↗
arXiv2011

K-Theories for Certain Infinite Rank Bundles

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite rank bundles in the families index theorem, and bundles with pseudodifferential operators as structure group. In this paper, we construct the corresponding K-theories for these types of bundles. We develop the formalism of these theories and use their Chern character to detect a large class of nontrivial elements.

math.KT↗
arXiv2009

The order of curvature operators on loop groups

For loop groups (free and based), we compute the exact order of the curvature operator of the Levi-Civita connection depending on a Sobolev space parameter. This extends results of Freed and Maeda-Rosenberg-Torres.

math.DG↗