40 citations · 436 across the 28 of their papers we have counts for
13 papers · 1 filter
Multiple-SLE connectivity weights for rectangles, hexagons, and octagons
Steven M. Flores, Jacob J. H. Simmons, Peter Kleban
In a previous article, we define "connectivity weights" to be functions with these two properties: 1) They solve the three conformal Ward identities of conformal field theory (CFT)…
A solution space for a system of null-state partial differential equations 4
Steven M. Flores, Peter Kleban
This article is the last of four that completely characterize a solution space for a homogeneous system of linear partial differential equations (PDEs) in $2…
A solution space for a system of null-state partial differential equations 2
Steven M. Flores, Peter Kleban
This article is the second of four that completely characterize a solution space for a homogeneous system of linear partial differential equations (PDEs) in…
A solution space for a system of null-state partial differential equations 3
Steven M. Flores, Peter Kleban
This article is the third of four that completely characterize a solution space for a homogeneous system of linear partial differential equations (PDEs) in $…
A solution space for a system of null-state partial differential equations 1
Steven M. Flores, Peter Kleban
In this first of four articles, we study a homogeneous system of linear partial differential equations (PDEs) in variables that arises in conformal field theory (CFT) a…
Cluster densities at 2-D critical points in rectangular geometries
Jacob J. H. Simmons, Peter Kleban, Steven M. Flores +1
Making use of a recent complete calculation of a chiral six-point correlation function C(z) in a rectangle we calculate various quantities of interest for percolation (SLE paramete…
New percolation crossing formulas and second-order modular forms
Nikolaos Diamantis, Peter Kleban
We consider the three new crossing probabilities for percolation recently found via conformal field theory by Simmons, Kleban and Ziff. We prove that all three of them (i) may be s…
Exact factorization of correlation functions in 2-D critical percolation
Jacob J. H. Simmons, Peter Kleban, Robert M. Ziff
By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are v…
Intervals Between Farey Fractions in the Limit of Infinite Level
Jan Fiala, Peter Kleban
The modified Farey sequence consists, at each level k, of rational fractions r_k^{(n)}, with n=1, 2, ...,2^k+1. We consider I_k^{(e)}, the total length of (one set of) alternate in…
Generalized Number Theoretic Spin Chain-Connections to Dynamical Systems and Expectation Values
Jan Fiala, Peter Kleban
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recurs…
Thermodynamics of the Farey Fraction Spin Chain
Jan Fiala, Peter Kleban
We consider the Farey fraction spin chain, a one-dimensional model defined on (the matrices generating) the Farey fractions. We extend previous work on the thermodynamics of this m…
Crossing Probabilities and Modular Forms
Peter Kleban, Don Zagier
We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic Löwn…
The Phase Transition in Statistical Models Defined on Farey Fractions
Jan Fiala, Peter Kleban, Ali Ozluk
We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as "spin chains", with long-range interactions, while another arises in t…