Related papers: Multiple Points of Gaussian Random Fields
We discuss the application of random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. We show that, under a number of different assumptions, the feasibility and…
We present higher-derivative gravities that propagate an arbitrary number of gravitons of different mass on (A)dS backgrounds. These theories have multiple critical points, at which the masses degenerate and the graviton energies are…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many…
We consider large-scale point fields which naturally appear in the context of the Kardar-Parisi-Zhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass concentration, and by shocks separating the sources…
In this work we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. 2007. In particular we focus on the one-point density probability distribution function of the mass density field in…
It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of of…
We prove the existence of $N$ distinct pairs of nontrivial solutions for critical $p$-Laplacian problems in ${\mathbb R}^N$, as well as in bounded domains. To overcome the difficulties arising from the lack of compactness, we use a recent…
In this paper, the focus will be on both the existence and non-existence respectively of finite critical trajectories and recurrent trajectories of a quadratic differential on the Riemann sphere. We show the connection between these two…
Let $\{X(t), t\in M\}$ and $\{Z(t'), t'\in M'\}$ be smooth Gaussian random fields parameterized on Riemannian manifolds $M$ and $M'$, respectively, such that $X(t) = Z(f(t))$, where $f: M \to M'$ is a diffeomorphic transformation. We study…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We discover a new tricritical point realized only in non-equilibrium steady states, using the AdS/CFT correspondence. Our system is a (3+1)-dimensional strongly-coupled large-$N_{c}$ gauge theory. The tricritical point is associated with a…
In this note we study the mean field equations for the $3d$ Random Field Ising Model. We discuss the phase diagram of the model, and we address the problem of finding if such equations admit more than one solution. We find two different…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
It is shown that $3$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with nearly minimum total Gaussian surface area must be close to adjacent $120$ degree sectors, when $n\geq2$. These same results hold for any…
We study the landscape complexity of the Hamiltonian $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a smooth Gaussian process with isotropic increments on $\mathbb R^{N}$. This model describes a single particle on a random potential in…
We extend the classical Garsia-Rodemich-Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint H\"older continuity along the rectangles for fractional Brownian fields $W(t, x)$ and for the…
The random-energy model is studied in the presence of random fields. The problem is solved exactly both in the microcanonical ensemble, without recourse to the replica method, and in the canonical ensemble using the replica formalism. The…
We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…
We explore the super-horizon evolution of the two-point and three-point correlation functions of the primordial density perturbation in randomly-generated multi-field potentials. We use the Transport method to evolve perturbations and give…