38 citations · 183 across the 18 of their papers we have counts for
18 papers
Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution
Dan Betea, Jérémie Bouttier, Harriet Walsh
We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universa…
Limit shapes for skew Howe duality
Dan Betea, Anton Nazarov, Travis Scrimshaw
We study large random partitions boxed into a rectangle and coming from skew Howe duality, or alternatively from dual Schur measures. As the sides of the rectangle go to infinity,…
Peaks of cylindric plane partitions
Dan Betea, Alessandra Occelli
We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their…
The half-space Airy stat process
Dan Betea, Patrik Ferrari, Alessandra Occelli
We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this…
Multicritical random partitions
Dan Betea, Jérémie Bouttier, Harriet Walsh
We study two families of probability measures on integer partitions, which are Schur measures with parameters tuned in such a way that the edge fluctuations are characterized by a…
Muttalib--Borodin plane partitions and the hard edge of random matrix ensembles
Dan Betea, Alessandra Occelli
We study probabilistic and combinatorial aspects of natural volume-and-trace weighted plane partitions and their continuous analogues. We prove asymptotic limit laws for the larges…
Discrete and continuous Muttalib--Borodin processes I: the hard edge
Dan Betea, Alessandra Occelli
In this note we study a natural measure on plane partitions giving rise to a certain discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttal…
Determinantal point processes from symplectic and orthogonal characters and applications
Dan Betea
We show that the symplectic and orthogonal character analogues of Okounkov's Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply th…
Stationary half-space last passage percolation
Dan Betea, Patrik L. Ferrari, Alessandra Occelli
In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close…
New edge asymptotics of skew Young diagrams via free boundaries
Dan Betea, Jérémie Bouttier, Peter Nejjar +1
We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Bai…
On the combinatorics of last passage percolation in a quarter square and fluctuations
Dan Betea
In this note we give a(nother) combinatorial proof of an old result of Baik--Rains: that for appropriately considered independent geometric weights, the generating series for last…
The periodic Schur process and free fermions at finite temperature
Dan Betea, Jérémie Bouttier
We revisit the periodic Schur process introduced by Borodin in 2007. Our contribution is threefold. First, we provide a new simpler derivation of its correlation functions via the…
Correlations for symplectic and orthogonal Schur measures
Dan Betea
We show, using either Fock space techniques or Macdonald difference operators, that certain symplectic and orthogonal analogues of Okounkov's Schur measure are determinantal with k…
The free boundary Schur process and applications I
Dan Betea, Jérémie Bouttier, Peter Nejjar +1
We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitr…
Perfect sampling algorithm for Schur processes
Dan Betea, Cédric Boutillier, Jérémie Bouttier +3
We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to cer…
Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures
D. Betea, M. Wheeler, P. Zinn-Justin
We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which…
Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
Dan Betea, Michael Wheeler
We prove and conjecture some new symmetric function identities, which equate the generating series of 1. Plane partitions, subject to certain restrictions and weightings, and 2. Al…
Elliptically Distributed Lozenge Tilings of a Hexagon
Dan Betea
We present a detailed study of a four parameter family of elliptic weights on tilings of a hexagon introduced by Borodin, Gorin and Rains, generalizing some of their results. In th…