Phase transitions in the onedimensional coulomb gas ensembles
(2018) In Annals of Applied Probability 28(2). p.12491291 Abstract
We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles... (More)
We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles in the limit when the number of particles goes to infinity. We identify 5 different phases for any positive temperature. The proofs rely on a conditional central limit theorem for nonidentical random variables, which has an interest on its own.
(Less)
 author
 Turova, Tatyana S. ^{LU}
 organization
 publishing date
 20180401
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Coulomb gas, Gibbs ensemble., Phase transitions
 in
 Annals of Applied Probability
 volume
 28
 issue
 2
 pages
 43 pages
 publisher
 Institute of Mathematical Statistics
 external identifiers

 scopus:85046253733
 ISSN
 10505164
 DOI
 10.1214/17AAP1329
 language
 English
 LU publication?
 yes
 id
 c33abb97df0f46398bd6cedd5a4e4bda
 date added to LUP
 20180517 15:20:27
 date last changed
 20200113 00:42:15
@article{c33abb97df0f46398bd6cedd5a4e4bda, abstract = {<p>We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles in the limit when the number of particles goes to infinity. We identify 5 different phases for any positive temperature. The proofs rely on a conditional central limit theorem for nonidentical random variables, which has an interest on its own.</p>}, author = {Turova, Tatyana S.}, issn = {10505164}, language = {eng}, month = {04}, number = {2}, pages = {12491291}, publisher = {Institute of Mathematical Statistics}, series = {Annals of Applied Probability}, title = {Phase transitions in the onedimensional coulomb gas ensembles}, url = {http://dx.doi.org/10.1214/17AAP1329}, doi = {10.1214/17AAP1329}, volume = {28}, year = {2018}, }