Joseph G. Conlon
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Joseph G. Conlon has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Michael Dabkowski
Department of Mathematics and Statistics, University of Michigan Dearborn, Dearborn, USA
8 shared publications - Arash Fahim
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
4 shared publications - Thomas Spencer
Institute for Advanced Study
3 shared publications - André Schlichting
Institute for Applied Analysis, Ulm University, Ulm, Germany
2 shared publications - Jingchen Wu2 shared publications
Michael Dabkowski
2 shared publications
Latest Publications
- Open Access
- 21 July 2025
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 192 (8) , 1-39
Extensions of the Brascamp-Lieb Inequality and the Dipole Gas
This paper is concerned with $$d\ge 2$$ lattice field models with action $$V(\nabla \phi (\cdot ))$$ , where $$V:\mathbb {R}^d\rightarrow \mathbb {R}$$ is a uniformly convex function. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.- 21 July 2025
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 192 (8) , 1-39
Open AccessExtensions of the Brascamp-Lieb Inequality and the Dipole Gas
This paper is concerned with $$d\ge 2$$ lattice field models with action $$V(\nabla \phi (\cdot ))$$ , where $$V:\mathbb {R}^d\rightarrow \mathbb {R}$$ is a uniformly convex function. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem. - Open Access
- 4 January 2025
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2025 (01-??) , 14-62
Properties of the Dirichlet Green's function for linear diffusions on a half line
This article concerns the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian. Formulas for the Dirichlet Green's function on the half line are only known in special cases. The main object of study in the paper is the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic behavior in the limit as the diffusion coefficient vanishes, and a log concavity result are obtained for this ratio. These results have been used in the proof of asymptotic behavior for a simple model of Ostwald ripening. For more information see https://ejde.math.txstate.edu/Volumes/2025/14/abstr.html
- 4 January 2025
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2025 (01-??) , 14-62
Open AccessProperties of the Dirichlet Green's function for linear diffusions on a half line
This article concerns the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian. Formulas for the Dirichlet Green's function on the half line are only known in special cases. The main object of study in the paper is the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic behavior in the limit as the diffusion coefficient vanishes, and a log concavity result are obtained for this ratio. These results have been used in the proof of asymptotic behavior for a simple model of Ostwald ripening. For more information see https://ejde.math.txstate.edu/Volumes/2025/14/abstr.html
- Open Access
Extensions of the Brascamp-Lieb Inequality and the Dipole Gas
This paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.
Open AccessExtensions of the Brascamp-Lieb Inequality and the Dipole Gas
This paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.
- 23 August 2022
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 32 (5) , 1-58
On Global Asymptotic Stability for the Diffusive Carr–Penrose Model
- 23 August 2022
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 32 (5) , 1-58
On Global Asymptotic Stability for the Diffusive Carr–Penrose Model
- Open Access
On Global Asymptotic Stability for the diffusive Carr-Penrose Model
This paper is concerned with large time behavior of the solution to a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. Like the LSW model, the Carr-Penrose model has a family of rapidly decreasing self-similar solutions, depending on a parameter $\beta$ with $0<\beta\le 1$. It is shown that if the initial data has compact support then the solution to the diffusive model at large time approximates the $\beta=1$ self-similar solution. This result supports the intuition that diffusion provides the mechanism whereby the $\beta=1$ self-similar solution of the LSW model is the only physically relevant one.Open AccessOn Global Asymptotic Stability for the diffusive Carr-Penrose Model
This paper is concerned with large time behavior of the solution to a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. Like the LSW model, the Carr-Penrose model has a family of rapidly decreasing self-similar solutions, depending on a parameter $\beta$ with $0<\beta\le 1$. It is shown that if the initial data has compact support then the solution to the diffusive model at large time approximates the $\beta=1$ self-similar solution. This result supports the intuition that diffusion provides the mechanism whereby the $\beta=1$ self-similar solution of the LSW model is the only physically relevant one. - 19 December 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 178 (2) , 420-471
Global Stability for a Class of Nonlinear PDE with Non-local Term
- 19 December 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 178 (2) , 420-471
Global Stability for a Class of Nonlinear PDE with Non-local Term
- 10 December 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 178 (1) , 117-177
On Global Asymptotic Stability for the LSW Model with Subcritical Initial Data
- 10 December 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 178 (1) , 117-177
On Global Asymptotic Stability for the LSW Model with Subcritical Initial Data
- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 39 (4) , 1821-1889
A non-local problem for the Fokker-Planck equation related to the Becker-Döring model
This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. The first main result concerns the well-posedness and regularity of the Cauchy problem. The well-posedness is based on a fixed point argument, and the regularity on Schauder estimates. The first a priori estimates yield Hölder regularity of the non-local order parameter, which is improved by an iteration argument. The asymptotic behavior of solutions depends on some order parameter$ \rho $ depending on the initial data. The system shows different behavior depending on a value$ \rho_s>0 $ , determined from the potentials and diffusion coefficient. For$ \rho \leq \rho_s $ , there exists an equilibrium solution$ c^ {{ \rm{eq}}} _{(\rho)} $ . If$ \rho\le\rho_s $ the solution converges strongly to$ c^ {{ \rm{eq}}} _{(\rho)} $ , while if$ \rho > \rho_s $ the solution converges weakly to$ c^ {{ \rm{eq}}} _{(\rho_s)} $ . The excess$ \rho - \rho_s $ gets lost due to the formation of larger and larger clusters. In this regard, the model behaves similarly to the classical Becker-Döring equation. The system possesses a free energy, strictly decreasing along the evolution, which establishes the long time behavior. In the subcritical case$ \rho<\rho_s $ the entropy method, based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates, is used to obtain explicit convergence rates to the equilibrium solution. The close connection of the presented model and the Becker-Döring model is outlined by a family of discrete Fokker-Planck type equations interpolating between both of them. This family of models possesses a gradient flow structure, emphasizing their commonality.- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 39 (4) , 1821-1889
A non-local problem for the Fokker-Planck equation related to the Becker-Döring model
This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. The first main result concerns the well-posedness and regularity of the Cauchy problem. The well-posedness is based on a fixed point argument, and the regularity on Schauder estimates. The first a priori estimates yield Hölder regularity of the non-local order parameter, which is improved by an iteration argument. The asymptotic behavior of solutions depends on some order parameter$ \rho $ depending on the initial data. The system shows different behavior depending on a value$ \rho_s>0 $ , determined from the potentials and diffusion coefficient. For$ \rho \leq \rho_s $ , there exists an equilibrium solution$ c^ {{ \rm{eq}}} _{(\rho)} $ . If$ \rho\le\rho_s $ the solution converges strongly to$ c^ {{ \rm{eq}}} _{(\rho)} $ , while if$ \rho > \rho_s $ the solution converges weakly to$ c^ {{ \rm{eq}}} _{(\rho_s)} $ . The excess$ \rho - \rho_s $ gets lost due to the formation of larger and larger clusters. In this regard, the model behaves similarly to the classical Becker-Döring equation. The system possesses a free energy, strictly decreasing along the evolution, which establishes the long time behavior. In the subcritical case$ \rho<\rho_s $ the entropy method, based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates, is used to obtain explicit convergence rates to the equilibrium solution. The close connection of the presented model and the Becker-Döring model is outlined by a family of discrete Fokker-Planck type equations interpolating between both of them. This family of models possesses a gradient flow structure, emphasizing their commonality.- Open Access
On Global Asymptotic Stability for the LSW Model with subcritical initial data
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The method of proof is along similar lines to the one used in a previous paper of the authors. This previous paper proves global asymptotic stability for a class of infinite dimensional dynamical systems for which no Lyapounov function is (apparently) available.
Open AccessOn Global Asymptotic Stability for the LSW Model with subcritical initial data
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The method of proof is along similar lines to the one used in a previous paper of the authors. This previous paper proves global asymptotic stability for a class of infinite dimensional dynamical systems for which no Lyapounov function is (apparently) available.
- Open Access
A non-local problem for the Fokker-Planck equation related to the Becker-Döring model
This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. The first main result concerns the well-posedness and regularity of the Cauchy problem. The well-posedness is based on a fixed point argument, and the regularity on Schauder estimates. The first a priori estimates yield H\"older regularity of the non-local order parameter, which is improved by an iteration argument. The asymptotic behavior of solutions depends on some order parameter $\rho$ depending on the initial data. The system shows different behavior depending on a value $\rho_s>0$, determined from the potentials and diffusion coefficient. For $\rho \leq \rho_s$, there exists an equilibrium solution $c^{\text{eq}}_{(\rho)}$. If $\rho\le\rho_s$ the solution converges strongly to $c^{\text{eq}}_{(\rho)}$, while if $\rho > \rho_s$ the solution converges weakly to $c^{\text{eq}}_{(\rho_s)}$. The excess $\rho - \rho_s$ gets lost due to the formation of larger and larger clusters. In this regard, the model behaves similarly to the classical Becker-D\"oring equation. The system possesses a free energy, strictly decreasing along the evolution, which establishes the long time behavior. In the subcritical case $\rho<\rho_s$ the entropy method, based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates, is used to obtain explicit convergence rates to the equilibrium solution. The close connection of the presented model and the Becker-D\"oring model is outlined by a family of discrete Fokker-Planck type equations interpolating between both of them. This family of models possesses a gradient flow structure, emphasizing their commonality.Open AccessA non-local problem for the Fokker-Planck equation related to the Becker-Döring model
This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. The first main result concerns the well-posedness and regularity of the Cauchy problem. The well-posedness is based on a fixed point argument, and the regularity on Schauder estimates. The first a priori estimates yield H\"older regularity of the non-local order parameter, which is improved by an iteration argument. The asymptotic behavior of solutions depends on some order parameter $\rho$ depending on the initial data. The system shows different behavior depending on a value $\rho_s>0$, determined from the potentials and diffusion coefficient. For $\rho \leq \rho_s$, there exists an equilibrium solution $c^{\text{eq}}_{(\rho)}$. If $\rho\le\rho_s$ the solution converges strongly to $c^{\text{eq}}_{(\rho)}$, while if $\rho > \rho_s$ the solution converges weakly to $c^{\text{eq}}_{(\rho_s)}$. The excess $\rho - \rho_s$ gets lost due to the formation of larger and larger clusters. In this regard, the model behaves similarly to the classical Becker-D\"oring equation. The system possesses a free energy, strictly decreasing along the evolution, which establishes the long time behavior. In the subcritical case $\rho<\rho_s$ the entropy method, based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates, is used to obtain explicit convergence rates to the equilibrium solution. The close connection of the presented model and the Becker-D\"oring model is outlined by a family of discrete Fokker-Planck type equations interpolating between both of them. This family of models possesses a gradient flow structure, emphasizing their commonality.