Related papers: Recoverable systems and the maximal hard-core mode…
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan et al [SODA 2017] studied the alphabet size needed for such…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
In this paper we study Hard-Core model on a Cayley tree. For a normal divisor of index four new conditions for uniqueness and non-uniqueness of weakly periodic Gibbs measures are found.
Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal…
A new lattice model is presented for correlated electrons on the unrestricted $4^L$-dimensional electronic Hilbert space $\otimes_{n=1}^L{\bf C}^4$ (where $L$ is the lattice length). It is a supersymmetric generalization of the Hubbard…
We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after…
We study the cubic wave equation in AdS_(d+1) (and a closely related cubic wave equation on S^3) in a weakly nonlinear regime. Via time-averaging, these systems are accurately described by simplified infinite-dimensional quartic Hamiltonian…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…
This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t-J model and a single-band Hubbard model with additional bond-charge interaction are investigated, respectively. Some rigorous upper…
The Gaussian Effective Potential (GEP) is shown to be a useful variational tool for the study of the magnetic properties of strongly correlated electronic systems. The GEP is derived for a single band Hubbard model on a two-dimensional…
In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective…
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the…
It was suggested by Rasolt and Te\v{s}anovi\'c that the Landau level quantization in isotropic superconductors could enhance superconductivity in a very strong magnetic field, above the upper critical field ($H_{c2}$). We derive a…
The continuous random energy model (CREM) is a toy model of disordered systems introduced by Bovier and Kurkova in 2004 based on previous work by Derrida and Spohn in the 80s. In a recent paper by Addario-Berry and Maillard, they raised the…
A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for…