Zobrazeno 1 - 10
of 121
pro vyhledávání: '"Bryc, Wlodzimierz"'
We characterize limit fluctuations of height functions of the totally asymmetric simple exclusion processes with open boundaries at the co-existence line under the stationary measures. The limit behavior of the height functions at the co-existence li
Externí odkaz:
http://arxiv.org/abs/2407.20835
We study Motzkin paths of length $L$ with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end poin
Externí odkaz:
http://arxiv.org/abs/2402.00265
Autor:
Bryc, Wlodzimierz, Wang, Yizao
Publikováno v:
ALEA, Lat. Am. J. Probab. Math. Stat. 21, 73-94 (2024)
We compute limit fluctuations of random Motzkin paths with arbitrary end-points as the length of the path tends to infinity.
Comment: Expanded version with additional details
Comment: Expanded version with additional details
Externí odkaz:
http://arxiv.org/abs/2304.12975
Autor:
Bryc, Wlodzimierz, Wesolowski, Jacek
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 representation involves maxima of lazy simple random walks and an auxiliary inde
Externí odkaz:
http://arxiv.org/abs/2304.07144
Autor:
Bryc, Wlodzimierz, Wang, Yizao
We consider Motzkin paths of length $L$, 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 length $L$ tends to infinity, the limit behaviors of (a) boundary measures
Externí odkaz:
http://arxiv.org/abs/2304.00924
Publikováno v:
Colloquium Mathematicum 170 (2022), 211--238
We introduce one-way flows in near algebras and two-way flows in double near algebras with two interrelated multiplications. We establish parametric representations of the one-way and two-way flows in terms of a single element of the algebra that we
Externí odkaz:
http://arxiv.org/abs/2007.03082
Autor:
Bryc, Wlodzimierz, Swieca, Marcin
Publikováno v:
Journal of Statistical Physics, 177 (2019), pp. 252-284
We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans, Hakim and Pa
Externí odkaz:
http://arxiv.org/abs/1904.09536
Autor:
Bryc, Włodzimierz, Wang, Yizao
Publikováno v:
Advances in Applied Mathematics 106 (2019) 96-116
It is known that after scaling a random Motzkin path converges to a Brownian excursion. We prove that the fluctuations of the counting processes of the ascent steps, the descent steps and the level steps converge jointly to linear combinations of two
Externí odkaz:
http://arxiv.org/abs/1807.10057
Publikováno v:
Probability and Mathematical Statistics 39 (2019) pp. 237-258
This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow us to construct additional variance functions from known ones. We cons
Externí odkaz:
http://arxiv.org/abs/1708.05343
Autor:
Bryc, Włodzimierz, Wang, Yizao
Publikováno v:
Annales de l'Institut Henri Poincare 55 (2019), pp. 2169-2194
We investigate the fluctuations of cumulative density of particles in the asymmetric simple exclusion process with respect to the stationary distribution (also known as the steady state), as a stochastic process indexed by $[0,1]$. In three phases of
Externí odkaz:
http://arxiv.org/abs/1707.07350