Author:
Carinci Gioia,Giardinà Cristian,Redig Frank,Sasamoto Tomohiro
Abstract
AbstractWe study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $$q\in (0,1)$$
q
∈
(
0
,
1
)
and where at most $$2j\in \mathbb {N}$$
2
j
∈
N
particles per site are allowed. The process is constructed from a $$(2j+1)$$
(
2
j
+
1
)
-dimensional representation of a quantum Hamiltonian with $$U_q(\mathfrak {sl}_2)$$
U
q
(
sl
2
)
invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(q, j), we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first q-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from a homogeneous product measure.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
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