- Brownian bridge restrict of path measures within the higher tail of KPZ fashions(arXiv)
Authors: Shirshendu Ganguly, Milind Hegde, Lingfu Zhang
Summary: For fashions within the KPZ universality class, such because the zero temperature mannequin of planar final passage-percolation (LPP) and the optimistic temperature mannequin of directed polymers, its higher tail habits has been a subject of current curiosity, with explicit give attention to the related path measures (i.e., geodesics or polymers). For Exponential LPP, diffusive fluctuation had been established in Basu-Ganguly. Within the directed panorama, the continuum restrict of LPP, the limiting Gaussianity at one level, in addition to of associated finite-dimensional distributions of the KPZ mounted level, had been established, utilizing actual formulation in Liu and Wang-Liu. It was additional conjectured in these works that the restrict of the corresponding geodesic needs to be a Brownian bridge. We show it in each zero and optimistic temperatures; for the latter, neither the one-point restrict nor the size of fluctuations was beforehand recognized. As an alternative of counting on formulation (that are nonetheless lacking within the optimistic temperature literature), our arguments are geometric and probabilistic, utilizing the outcomes on the form of the load and free power profiles below the higher tail from Ganguly-Hegde as a place to begin. One other key ingredient entails novel coalescence estimates, developed utilizing the lately found shift-invariance Borodin-Gorin-Wheeler in these fashions. Lastly, our proof additionally yields perception into the construction of the polymer measure below the higher tail conditioning, establishing a quenched localization exponent round a random spine.
2. Native Statistics and Focus for Non-intersecting Brownian Bridges With Easy Boundary Knowledge(arXiv)
Authors: Amol Aggarwal, Jiaoyang Huang
Summary: On this paper we take into account non-intersecting Brownian bridges, below pretty normal higher and decrease boundaries, and beginning and ending information. Underneath the belief that these boundary information induce a clean restrict form (with out empty sides), we set up two outcomes. The primary is an almost optimum focus sure for the Brownian bridges on this mannequin. The second is that the majority native statistics of those bridges alongside any mounted time converge to the sine course of
