# Spectral gap for an unrestricted Kawasaki type dynamics

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 145-181
- ISSN: 1292-8100

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topPosta, Gustavo. "Spectral gap for an unrestricted Kawasaki type dynamics ." ESAIM: Probability and Statistics 1 (2010): 145-181. <http://eudml.org/doc/197732>.

@article{Posta2010,

abstract = {
We give an accurate asymptotic estimate for the gap of the generator
of a particular interacting particle system. The model we consider
may be informally described as follows. A certain number
of charged particles moves on the segment [1,L] according to
a Markovian law. One unitary charge, positive or negative,
jumps from a site k to another site k'=k+1 or k'=k-1 at a rate
which depends on the charge at site k and at site k'. The total
charge of the system is preserved by the dynamics, in this sense
our dynamics is similar to the Kawasaki dynamics, but in our case
there is no restriction on the maximum charge allowed per site.
The model is equivalent to an interface dynamics connected with
the stochastic Ising model at very low temperature: the “unrestricted
solid on solid model”. Thus the results we obtain may be read as
results for this model. We give necessary and sufficient conditions
to ensure that the spectral gap tends towards zero as the
inverse of the square of L, independently of the total charge.
We follow the method outlined in some papers by Yau (Lu, Yau (1993),
Yau (1994)) where a similar spectral gap is proved for the
original Kawasaki dynamics.
},

author = {Posta, Gustavo},

journal = {ESAIM: Probability and Statistics},

keywords = {Kawasaki dynamics / SOS model / spectral gap.; Kawasaki dynamics; SOS model; spectral gap; Ising model; interacting particle system},

language = {eng},

month = {3},

pages = {145-181},

publisher = {EDP Sciences},

title = {Spectral gap for an unrestricted Kawasaki type dynamics },

url = {http://eudml.org/doc/197732},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Posta, Gustavo

TI - Spectral gap for an unrestricted Kawasaki type dynamics

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 145

EP - 181

AB -
We give an accurate asymptotic estimate for the gap of the generator
of a particular interacting particle system. The model we consider
may be informally described as follows. A certain number
of charged particles moves on the segment [1,L] according to
a Markovian law. One unitary charge, positive or negative,
jumps from a site k to another site k'=k+1 or k'=k-1 at a rate
which depends on the charge at site k and at site k'. The total
charge of the system is preserved by the dynamics, in this sense
our dynamics is similar to the Kawasaki dynamics, but in our case
there is no restriction on the maximum charge allowed per site.
The model is equivalent to an interface dynamics connected with
the stochastic Ising model at very low temperature: the “unrestricted
solid on solid model”. Thus the results we obtain may be read as
results for this model. We give necessary and sufficient conditions
to ensure that the spectral gap tends towards zero as the
inverse of the square of L, independently of the total charge.
We follow the method outlined in some papers by Yau (Lu, Yau (1993),
Yau (1994)) where a similar spectral gap is proved for the
original Kawasaki dynamics.

LA - eng

KW - Kawasaki dynamics / SOS model / spectral gap.; Kawasaki dynamics; SOS model; spectral gap; Ising model; interacting particle system

UR - http://eudml.org/doc/197732

ER -

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