Related papers: Multiscale analysis of the conductivity in the Lor…
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace model introduced by Scarabotti. Writing…
We consider the Airy$_1$ process, which is the limit process in KPZ growth models with flat and non-random initial conditions. We study the persistence probability, namely the probability that the process stays below a given threshold $c$…
We prove a polynomial upper bound for the localization length of the Lorentz mirror model and the Manhattan model on the even cylinder. The main input is a conditional cylinder-localization theorem in the winding regime: if short-direction…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be…
This paper gives a complete description of the solutions of the one dimensional Ginzburg-Landau equations which model superconductivity phenomena in infinite slabs. We investigate this problem over the entire range of physically important…
We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine,…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
We investigate the optical conductivity of a Hubbard ring in presence of an impurity by means of exact diagonalization using the Lanczos algorithm. We concentrate thereby on the first excited, open shell state, i.e. on twisted boundary…
Let S_n be the set of all permutations on [n]:={1,2,....,n}. We denote by kappa_n the smallest cardinality of a subset A of S_{n+1} that "covers" S_n, in the sense that each pi in S_n may be found as an order-isomorphic subsequence of some…
This paper focuses on using the first curvature $\kappa(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al.,…
Assuming that $GCH$ holds and $\kappa$ is $\kappa^{+3}$-supercompact, we construct a generic extension $W$ of $V$ in which $\kappa$ remains strongly inaccessible and $(\alpha^+)^{HOD} < \alpha^+$ for every infinite cardinal $\alpha <…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…
Sparse autoencoders (SAEs) decompose transformer residual streams into interpretable feature dictionaries, yet the relationship between SAE width and causal influence on model output has not been systematically characterised. We introduce…
We consider a multiscale Boolean percolation on $\mathbb R^d$ with radius distribution $\mu$ on $[1,+\infty)$, $d\ge 2$. The model is defined by superposing the original Boolean percolation model with radius distribution $\mu$ with a…
The conformal mapping w=(L/2\pi)\ln z transforms the critical plane with a radial perturbation \alpha\rho^{-y} into a cylinder with width L and a constant deviation \alpha(2\pi/L)^y from the bulk critical point when the decay exponent y is…
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for…
We construct generally applicable small-loss rate expansions for the density operator of an open system. Successive terms of those expansions yield characteristic loss rates for dissipation processes. Three applications are presented in…
In the loop $O(n)$ model a collection of mutually-disjoint self-avoiding loops is drawn at random on a finite domain of a lattice with probability proportional to $${\lambda^{\# \mbox{edges}} n^{\# \mbox{loops}},}$$ where $\lambda, n \in…