Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Alberts, Tom"'
We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central charge $c \leq 1$. In this framework we introduce
Externí odkaz:
http://arxiv.org/abs/2407.08220
We build a regular version of the field $Z_{\beta}(t,x|s,y)$ which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing on $\mathbb{R}^{1+1}$: $\partial_t Z_{\beta}(t,x | s,y) =$ $\fr
Externí odkaz:
http://arxiv.org/abs/2208.11255
We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system that gove
Externí odkaz:
http://arxiv.org/abs/2011.05714
Autor:
Alberts, Tom, Normand, Raoul
We study the dimension properties of the spectral measure of the Circular $\beta$-Ensembles. For $\beta \geq 2$ it it was previously shown by Simon that the spectral measure is almost surely singular continuous with respect to Lebesgue measure on $\p
Externí odkaz:
http://arxiv.org/abs/1912.07788
Autor:
Alberts, Tom, Cator, Eric
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine the domains of the various pieces, which are the subsets of the weigh
Externí odkaz:
http://arxiv.org/abs/1907.00407
We prove that given any fixed asymptotic velocity, the finite length O'Connell-Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a Markovian property of the quenched polymer this reduces to showing th
Externí odkaz:
http://arxiv.org/abs/1905.13353
Autor:
Alberts, Tom, Clark, Jeremy
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter $n$, counting t
Externí odkaz:
http://arxiv.org/abs/1602.06629
We study the backwards Markov chain for the Bak-Sneppen model of biological evolution and derive its corresponding reversibility equations. We show that, in contrast to the forwards Markov chain, the dynamics of the backwards chain explicitly involve
Externí odkaz:
http://arxiv.org/abs/1510.04114
We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\leq s$ previo
Externí odkaz:
http://arxiv.org/abs/1508.04791