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Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
The $\beta$-ensembles of random matrix theory with classical weights have many special properties. One is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at general order of the…
In this paper, we obtain a local limit theorem for the Kemperman's model of oscillating random walk on $\mathbb{Z}$; it extends the existing results for classical random walks on $\mathbb Z$ or reflected random walks on $\mathbb N_0$. The…
Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we…
We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the…
Modules were introduced as an extension of Boolean automata networks. They have inputs which are used in the computation said modules perform, and can be used to wire modules with each other. In the present paper we extend this new…
Among the lattice loop models defined by Pearce, Rasmussen and Zuber (2006), the model corresponding to critical dense polymers ($\beta = 0$) is the only one for which an inversion relation for the transfer matrix $D_N(u)$ was found by…
Feedback optimization has emerged as an effective strategy for steady-state optimization of dynamical systems. By exploiting models of the steady-state input-output sensitivity, methods of this type are often sample efficient, and their use…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the…
The Ising model with ferromagnetic interactions that decay as $1/r^\alpha$ is analyzed in the non-extensive regime $0\leq\alpha\leq d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model…
Recent experiments on atomic-scale metallic contacts have shown that the quantization of the conductance appears clearly only after the average of the experimental results. Motivated by these results we have analyzed a simplified model…
Another Bell test "loophole" - imperfect rotational invariance - is explored, and novel realist ideas on parametric down-conversion as used in recent "quantum entanglement" experiments are presented. The usual quantum theory of entangled…
Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However,…
Up to now, future neutrino beam experiments have been designed and optimized in order to look for CP violation, \theta_{13} and the mass hierarchy under the conservative assumption that \theta_{13} is very small. However, the recent results…
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive…
The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the…
We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1--e --$\beta$ , where $\beta$ is a positive and fixed parameter. The positions of…
We numerically study the dynamics and stationary states of a spin ensemble strongly coupled to a single-mode resonator subjected to loss and external driving. Employing a generalized cumulant expansion approach we analyze finite-size…