160 citations · 688 across the 49 of their papers we have counts for
51 papers
Limits of Random Motzkin paths with KPZ related asymptotics
Wlodzimierz Bryc, Alexey Kuznetsov, Jacek Wesolowski
We study Motzkin paths of length with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin pat…
Fluctuations of random Motzkin paths II
Wlodzimierz Bryc, Yizao Wang
We compute limit fluctuations of random Motzkin paths with arbitrary end-points as the length of the path tends to infinity.
Pitman's discrete theorem for arbitrary initial laws and continuous time limits
Wlodzimierz Bryc, Jacek Wesolowski
We discuss Pitman's representation of a Markov process, which serves as a discrete analog to the Bessel 3D process starting at time 0 from an arbitrary initial law. This representa…
Limit theorems for random Motzkin paths near boundary
Wlodzimierz Bryc, Yizao Wang
We consider Motzkin paths of length , not fixed at zero at both end points, with constant weights on the edges and general weights on the end points. We investigate, as the leng…
From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval
Wlodek Bryc, Yizao Wang, Jacek Wesolowski
Barraquand and Le~Doussal introduced a family of stationary measures for the (conjectural) KPZ fixed point on an interval with Neumann boundary conditions, and predicted that they…
Markov limits of steady states of the KPZ equation on an interval
Wlodek Bryc, Alexey Kuznetsov
This paper builds upon the research of Corwin and Knizel who proved the existence of stationary measures for the KPZ equation on an interval and characterized them through a Laplac…