More Like this

1. Equilibria of time‐inconsistent stopping for one‐dimensional diffusion processes

   https://doi.org/10.1111/mafi.12385  

   Bayraktar, Erhan; Wang, Zhenhua; Zhou, Zhou (July 2023, Mathematical Finance)

   Abstract We consider three equilibrium concepts proposed in the literature for time‐inconsistent stopping problems, including mild equilibria (introduced in Huang and Nguyen‐Huu (2018)), weak equilibria (introduced in Christensen and Lindensjö (2018)), and strong equilibria (introduced in Bayraktar et al. (2021)). The discount function is assumed to be log subadditive and the underlying process is one‐dimensional diffusion. We first provide necessary and sufficient conditions for the characterization of weak equilibria. The smooth‐fit condition is obtained as a by‐product. Next, based on the characterization of weak equilibria, we show that an optimal mild equilibrium is also weak. Then we provide conditions under which a weak equilibrium is strong. We further show that an optimal mild equilibrium is also strong under a certain condition. Finally, we provide several examples including one showing a weak equilibrium may not be strong, and another one showing a strong equilibrium may not be optimal mild. 

   more » « less
2. Critical value asymptotics for the contact process on random graphs

   https://doi.org/10.1090/tran/8399  

   Nam, Danny; Nguyen, Oanh; Sly, Allan (January 2022, Transactions of the American Mathematical Society)

   Recent progress in the study of the contact process (see Shankar Bhamidi, Danny Nam, Oanh Nguyen, and Allan Sly [Ann. Probab. 49 (2021), pp. 244–286]) has verified that the extinction-survival threshold λ 1 \lambda _1 on a Galton-Watson tree is strictly positive if and only if the offspring distribution ξ \xi has an exponential tail. In this paper, we derive the first-order asymptotics of λ 1 \lambda _1 for the contact process on Galton-Watson trees and its corresponding analog for random graphs. In particular, if ξ \xi is appropriately concentrated around its mean, we demonstrate that λ 1 ( ξ ) ∼ 1 / E ξ \lambda _1(\xi ) \sim 1/\mathbb {E} \xi as E ξ → ∞ \mathbb {E}\xi \rightarrow \infty , which matches with the known asymptotics on d d -regular trees. The same results for the short-long survival threshold on the Erdős-Rényi and other random graphs are shown as well. 

   more » « less
3. Decomposition and the Gross–Taylor string theory

   https://doi.org/10.1142/S0217751X23501567  

   Pantev, Tony; Sharpe, Eric (October 2023, International Journal of Modern Physics A)

   It was recently argued by Nguyen, Tanizaki and Ünsal that two-dimensional pure Yang–Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper, we compare this decomposition to the Gross–Taylor expansion of two-dimensional pure [Formula: see text] Yang–Mills theory in the large-[Formula: see text] limit as the string field theory of a sigma model. Specifically, we study the Gross–Taylor expansion of individual Nguyen–Tanizaki–Ünsal universes. These differ from the Gross–Taylor expansion of the full Yang–Mills theory in two ways: a restriction to single instanton degrees, and some additional contributions not present in the expansion of the full Yang–Mills theory. We propose to interpret the restriction to single instanton degrees as implying a constraint, namely that the Gross–Taylor string has a global (higher-form) symmetry with Noether current related to the worldsheet instanton number. We compare two-dimensional pure Maxwell theory as a prototype obeying such a constraint, and also discuss in that case an analogue of the Witten effect arising under two-dimensional theta angle rotation. We also propose a geometric interpretation of the additional terms, in the special case of Yang–Mills theories on 2-spheres. In addition, also for the case of theories on 2-spheres, we propose a reinterpretation of the terms in the Gross–Taylor expansion of the Nguyen–Tanizaki–Ünsal universes, replacing sigma models on branched covers by counting disjoint unions of stacky copies of the target Riemann surface, that makes the Nguyen–Tanizaki–Ünsal decomposition into invertible field theories more nearly manifest. As the Gross–Taylor string is a sigma model coupled to worldsheet gravity, we also briefly outline the tangentially related topic of decomposition in two-dimensional theories coupled to gravity. 

   more » « less
4. Green function for linearized Navier–Stokes around a boundary shear layer profile for long wavelengths

   https://doi.org/10.4171/aihpc/64  

   Grenier, Emmanuel; Nguyen, Toan T (October 2023, Annales de l'Institut Henri Poincaré C, Analyse non linéaire)

   This paper is the continuation of a program, initiated in Grenier and Nguyen [SIAM J.Math. Anal. 51 (2019); J. Differential Equations 269 (2020)], to derive pointwise estimates on theGreen function of Orr–Sommerfeld equations. In this paper we focus on long wavelength perturbations, more precisely horizontal wave numbers\alphaof order\nu^{1/4}, which correspond to the lower boundary of the instability area for monotonic profiles. 

   more » « less
5. We need to know more about CTE teachers

   https://doi.org/10.1177/00317217231161535  

   Anglum, J Cameron; Diemer, Andrew R.; Ecton, Walter G.; Nguyen, Tuan D. (March 2023, Phi Delta Kappan)

   Over the past year, debates over the prevalence, distribution, and effects of teacher vacancy and underqualification have dominated many education narratives. Authors J. Cameron Anglum, Andrew R. Diemer, Walter G. Ecton, and Tuan D. Nguyen consider these debates in the context of growing interest in career and technical education (CTE) in high school settings. Research on secondary CTE teachers, including the quantification of teacher shortages in specific CTE content areas, remains insufficient to inform effective recruitment and retention policies. This dearth of scholarship on CTE teachers undermines the improvement of CTE programs. 

   more » « less