Zobrazeno 1 - 10
of 80
pro vyhledávání: '"60K35, 82B41"'
Autor:
Liu, Yucheng, Slade, Gordon
We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of the finite-
Externí odkaz:
http://arxiv.org/abs/2412.05503
Autor:
Henning, Florian, Kuelske, Christof
We provide a general theory of height-offset variables and their properties for nearest-neighbor integer-valued gradient models on trees. This notion goes back to Sheffield [25], who realized that such tail-measurable variables can be used to associa
Externí odkaz:
http://arxiv.org/abs/2411.13465
In this work, we consider the scaling limit of loop-erased random walk (LERW) in three dimensions and prove that the limiting occupation measure is equivalent to its $\beta$-dimensional Minkowski content, where $\beta \in (1, 5/3]$ is its Hausdorff d
Externí odkaz:
http://arxiv.org/abs/2403.07256
Autor:
Das, Sayan, Serio, Christian
We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit description,
Externí odkaz:
http://arxiv.org/abs/2402.16834
We derive sub-Gaussian bounds for the annealed transition density of the simple random walk on a high-dimensional loop-erased random walk. The walk dimension that appears in these is the exponent governing the space-time scaling of the process with r
Externí odkaz:
http://arxiv.org/abs/2312.09522
The disordered ferromagnet is a disordered version of the ferromagnetic Ising model in which the coupling constants are non-negative quenched random. A ground configuration is an infinite-volume configuration whose energy cannot be reduced by finite
Externí odkaz:
http://arxiv.org/abs/2309.06437
Autor:
Liu, Yucheng
Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic e
Externí odkaz:
http://arxiv.org/abs/2210.15580
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We consider an alt
Externí odkaz:
http://arxiv.org/abs/2203.06133
Autor:
Croydon, David A., Shiraishi, Daisuke
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial location of t
Externí odkaz:
http://arxiv.org/abs/2104.03459
Autor:
Ryan, Kieran
Publikováno v:
Journal of Statistical Physics, Volume 185, Article number: 7 (2021)
We study the Manhattan and Lorentz Mirror models on an infinite cylinder of finite even width $n$, with the mirror probability $p$ satisfying $p
Externí odkaz:
http://arxiv.org/abs/2010.03609