Related papers: Interacting Brownian motions in infinite dimension…
We solve the infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles in $ \mathbb{R}^+$ interacting through the two-dimensional Coulomb potential. The equilibrium states of the…
We solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles interacting via two-dimensional Coulomb potentials. The equilibrium states of the associated unlabeled stochastic…
We prove the convergence of $ \nN $-particle systems of Brownian particles with logarithmic interaction potentials onto a system described by the infinite-dimensional stochastic differential equation (ISDE). % For this proof we present two…
The Airy$_{\beta }$ random point fields ($ \beta = 1,2,4$) are random point fields emerging as the soft-edge scaling limits of eigenvalues of Gaussian random matrices. We construct the unlabeled diffusion reversible with respect to the…
We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs…
We study the infinite-dimensional stochastic differential equations (ISDEs) of infinite-particle systems associated with Coulomb random point fields. The stochastic dynamics described by these ISDEs are referred to as Coulomb interacting…
We prove that the tagged particles of infinitely many Brownian particles in $ \Rtwo $ interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature $ \beta = 2 $ are sub-diffusive. The associated delabeled…
We study a quasi-statically driven random field Ising model (RFIM) at zero temperature with interactions mediated by the long-range anisotropic Eshelby kernel. Analogously to amorphous solids at their yielding transition, and differently…
We consider certain random matrix eigenvalue dynamics, akin to Dyson Brownian motion, introduced by Rider and Valko. We show that from every initial condition, including ones involving coinciding coordinates, the dynamics, enhanced with…
Recently, there has been significant interest in understanding the properties of Markov random fields (M.r.f.) defined on the independent sets of sparse graphs. When these M.r.f. are restricted to pairwise interactions (i.e. hardcore…
We study the convergence properties of Glauber dynamics for the random field Ising model (RFIM) with ferromagnetic interactions on finite domains of $\mathbb{Z}^d$, $d \ge 2$. Of particular interest is the Griffiths phase where correlations…
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial…
We use the RG framework set up in arXiv:2009.10087 to explore the $\phi^3$ theory with a random field interaction. According to the Parisi-Sourlas conjecture this theory admits a fixed point with emergent supersymmetry which is related to…
We show how minimally-coupled matter fields of arbitrary spin, when coupled to Ricci-Based Gravity theories, develop non-trivial effective interactions that can be treated perturbatively only below a characteristic high-energy scale…
The matrix equations of the random-phase approximation (RPA) are derived for the point-coupling Lagrangian of the relativistic mean-field (RMF) model. Fully consistent RMF plus (quasiparticle) RPA illustrative calculations of the isoscalar…
In a recent letter, Fytas et al. [Phys. Rev. Lett. 122, 240603 (2019)] study the critical point of the equilibrium random-field Ising model (RFIM) in $D=5$ by means of state-of-art zero-temperature lattice simulations. We show that their…
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power $2-\alpha$ (for $0 \leq \alpha < 1$), and prepared with randomly chosen boundary conditions. We show that at low…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to…