Related papers: Approximating the satisfiability threshold for ran…
Understanding the statistics of level crossings in stochastic processes is crucial across many scientific disciplines. The traditional Kac-Rice formula gives the mean rate of level crossings and has found broad use. However, that mean rate…
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase transition in Bernoulli percolation. In addition to…
We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable…
We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show that the mean number of fixed points can be calculated as the…
We study the total variation (TV) distance between the laws of the 2D Ising/FK-Ising model in a box of side-length $N$ with and without an i.i.d.\ Gaussian external field with variance $\epsilon^2$. Letting the external field strength…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
We study the relativistic O(N) field theory near the quantum critical point in 2+1 dimensions for N=2 and N=3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a peak associated with the…
We investigate the collective dynamics of a population of XY model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or negative value, and subject to thermal noise controlled by…
The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase…
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently,…
We define an ensemble of random Clifford quantum circuits whose output state undergoes an entanglement phase transition between two volume-law phases as a function of measurement rate. Our setup maps exactly the output state to the ground…
In this note I will review some of the recent results that have been obtained in the probabilistic approach to the random satisfiability problem. At the present moment the results are only heuristic. In the case of the random…
We consider a threshold factor model for high-dimensional time series in which the dynamics of the time series is assumed to switch between different regimes according to the value of a threshold variable. This is an extension of threshold…
Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…
In this work we have studied the QCD phase structure and critical dynamics related to the 3-$d$ $O(4)$ and $Z(2)$ symmetry universality classes in the two-flavor quark-meson low energy effective theory within the functional renormalization…
We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in…
We give the first efficient algorithm to approximately count the number of solutions in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previous counting algorithm for the permissive version…
The global center symmetry of quenched QCD at zero baryonic chemical potential is broken spontaneously at a critical temperature $T_c$ leading to a first-order phase transition. Including heavy dynamical quarks breaks the center symmetry…
Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-bodysystems. This is a highly challenging task as the fragility of quantum states to external perturbations…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…