Exact results for an asymmetric annihilation process with open boundaries (2009)
Ayyer, Arvind, Mallick, Kirone
We consider a nonequilibrium reaction-diffusion model on a finite one dimensional lattice with bulk and boundary dynamics inspired by Glauber dynamics of the Ising model. We show that the model has a...
A Protobijection between Alternating Sign Matrices and Descending Plane Partitions (2009)
We construct a direct natural bijection between descending plane partitions without any special part and permutations. The directness is in the sense that the bijection avoids any reference to...
Two Dimensional Directed Lattice Walks with Boundaries (2008)
Arvind Ayyer, Doron Zeilberger
We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two...
A bijectional attack on the Razumov-Stroganov conjecture (2008)
Ayyer, Arvind, Zeilberger, Doron
We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.
On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries (2008)
Ayyer, Arvind, Lebowitz, Joel L., Speer, Eugene R.
We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles, as well as vacancies (holes), on L sites of a one-dimensional lattice in...
QUENCHED CLT FOR RANDOM TORAL AUTOMORPHISM (2008)
Arvind Ayyer, Carlangelo Liverani, Mikko Stenlund
Abstract. We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT...
Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms, Chaos (2008)
Abstract. We consider pairs of toral automorphisms (A, B) satisfying an invariant cone property. At each iteration, A acts with probability p ∈ (0, 1) and B with probability 1 − p. We prove...
A bijectional attack on the Razumov-Stroganov conjecture (2008)
Arvind Ayyer, Doron Zeilberger
We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture. 1
Quenched CLT for random toral automorphism (2007)
Ayyer, Arvind, Liverani, Carlangelo, Stenlund, Mikko
We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the...
The Half-Perimeter Generating Function of Gated and Wicketed Ferrers diagrams (2007)
We show that the half-perimeter generating functions for the number of Wicketed and Gated Ferrers diagrams is algebraic. Furthermore, the generating function of the Wicketed Ferrers diagrams is...
Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms (2007)
Ayyer, Arvind, Stenlund, Mikko
We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p and B with probability 1-p. We prove exponential decay of...
Two Dimensional Directed Lattice Walks with Boundaries (2007)
Ayyer, Arvind, Zeilberger, Doron
We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two...
Arvind Ayyer, Doron Zeilberger
We show that the generating function (in n) for the number of walks on the square lattice with steps (1, 1), (1, −1), (2, 2) and (2, −2) from (0, 0) to (2n, 0) in the region 0 ≤ y ≤ w...
Ayyer, Arvind, Zeilberger, Doron
We show that the generating function (in n) for the number of walks on the square lattice with steps (1,1), (1,-1), (2,2) and (2,-2) from (0,0) to (2n,0) in the region 0
Towards The Moduli Space of Extended Partial Isometries (2005)
Amdeberhan, Tewodros, Ayyer, Arvind
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which...
Energy transfer and locality in magnetohydrodynamic turbulence (2003)
Verma, Mahendra K., Ayyer, Arvind, Chandra, Amar V.
The shell-to-shell energy transfer rates for magnetohydrodynamic (MHD) turbulence are computed analytically, which shows local energy transfer rates from velocity to velocity, velocity to magnetic,...
Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence (2002)
Verma, Mahendra K., Ayyer, Arvind, Debliquy, Olivier, Kumar, Shishir, Chandra, Amar V.
In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wavenumber shells in incompressible fluid turbulence. The computation has...