Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Liechty, Karl"'
Autor:
Gharakhloo, Roozbeh, Liechty, Karl
Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal polynomials, co
Externí odkaz:
http://arxiv.org/abs/2401.01971
Autor:
Gorin, Vadim, Liechty, Karl
We study the behavior of configurations in the symmetric six-vertex model with $a,b,c$ weights in the $n\times n$ square with Domain Wall Boundary Conditions as $n\to\infty$. We prove that when $\Delta=\frac{a^2+b^2-c^2}{2ab}<1$, configurations near
Externí odkaz:
http://arxiv.org/abs/2310.12735
Autor:
Liechty, Karl, Petersen, T. Kyle
For a fixed irrational number $\alpha$ and $n\in \mathbb{N}$, we look at the shape of the sequence $(f(1),\ldots,f(n))$ after Schensted insertion, where $f(i) = \alpha i \mod 1$. Our primary result is that the boundary of the Schensted shape is appro
Externí odkaz:
http://arxiv.org/abs/2107.11515
Publikováno v:
Ann. Inst. H. Poincar\'e Probab. Stat. 58 (4), 2250-2283 (2022)
We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting Brownian bridges as $N\to\infty$, where the first $N-m$ pa
Externí odkaz:
http://arxiv.org/abs/2009.07781
Autor:
Geronimo, Jeffrey S., Liechty, Karl
Publikováno v:
Advances in Mathematics 365 (2020): 107064
The Fourier extension method, also known as the Fourier continuation method, is a method for approximating non-periodic functions on an interval using truncated Fourier series with period larger than the interval on which the function is defined. Whe
Externí odkaz:
http://arxiv.org/abs/1901.03453
Autor:
Buckingham, Robert, Liechty, Karl
The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson sea on th
Externí odkaz:
http://arxiv.org/abs/1709.07141
Autor:
Buckingham, Robert, Liechty, Karl
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle conditioned to sta
Externí odkaz:
http://arxiv.org/abs/1707.07211
Autor:
Liechty, Karl, Wang, Dong
We derive the local statistics of the canonical ensemble of free fermions in a quadratic potential well at finite temperature, as the particle number approaches infinity. This free fermion model is equivalent to a random matrix model proposed by Mosh
Externí odkaz:
http://arxiv.org/abs/1706.06653
Autor:
Bleher, Pavel, Liechty, Karl
We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal formula for
Externí odkaz:
http://arxiv.org/abs/1702.01190
Autor:
Liechty, Karl, Wang, Dong
We study a model of nonintersecting Brownian bridges on an interval with either absorbing or reflecting walls at the boundaries, focusing on the point in space-time at which the particles meet the wall. These processes are determinantal, and in diffe
Externí odkaz:
http://arxiv.org/abs/1608.08712