Zobrazeno 1 - 10
of 176
pro vyhledávání: '"Hammond, Alan"'
Autor:
Fribergh, Alexander, Hammond, Alan
We consider supercritical bond percolation in $\mathbb{Z}^d$ for $d \geq 3$. The origin lies in a finite open cluster with positive probability, and, when it does, the diameter of this cluster has an exponentially decaying tail. For each unit vector
Externí odkaz:
http://arxiv.org/abs/2408.16636
Autor:
Hammond, Alan, Helmuth, Tyler
We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the tori we c
Externí odkaz:
http://arxiv.org/abs/2306.03064
Autor:
Hammond, Alan
We study random-turn resource-allocation games. In the Trail of Lost Pennies, a counter moves on $\mathbb{Z}$. At each turn, Maxine stakes $a \in [0,\infty)$ and Mina $b \in [0,\infty)$. The counter $X$ then moves adjacently, to the right with probab
Externí odkaz:
http://arxiv.org/abs/2209.07451
In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed subset of the
Externí odkaz:
http://arxiv.org/abs/2206.08300
For an $n$-element subset $U$ of $\mathbb{Z}^2$, select $x$ from $U$ according to harmonic measure from infinity, remove $x$ from $U$, and start a random walk from $x$. If the walk leaves from $y$ when it first enters $U$, add $y$ to $U$. Iterating t
Externí odkaz:
http://arxiv.org/abs/2110.13895
In 2002, Johansson conjectured that the maximum of the Airy$_2$ process minus the parabola $x^2$ is almost surely achieved at a unique location. This result was proved a decade later by Corwin and Hammond; Moreno Flores, Quastel and Remenik; and Pime
Externí odkaz:
http://arxiv.org/abs/2101.04205
Autor:
Ganguly, Shirshendu, Hammond, Alan
Many complex statistical mechanical models have intricate energy landscapes. The ground state, or lowest energy state, lies at the base of the deepest valley. In examples such as spin glasses and Gaussian polymers, there are many valleys; the abundan
Externí odkaz:
http://arxiv.org/abs/2010.05837
Autor:
Ganguly, Shirshendu, Hammond, Alan
The energy and geometry of maximizing paths in integrable last passage percolation models are governed by the characteristic KPZ scaling exponents of one-third and two-thirds. When represented in scaled coordinates that respect these exponents, this
Externí odkaz:
http://arxiv.org/abs/2010.05836
In discrete planar last passage percolation (LPP), random values are assigned independently to each vertex in $\mathbb Z^2$, and each finite upright path in $\mathbb Z^2$ is ascribed the weight given by the sum of values of its vertices. The weight o
Externí odkaz:
http://arxiv.org/abs/2006.11448