Related papers: Critical Brownian multiplicative chaos
Gauging a finite Abelian normal subgroup $\Gamma$ of a nonanomalous 0-form symmetry $G$ of a theory in $(d+1)$D spacetime can yield an unconventional critical point if the original theory has a continuous transition where $\Gamma$ is…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
In the present paper, we show that (under some minor technical assumption) Complex Gaussian Multiplicative Chaos defined as the complex exponential of a $\log$-correlated Gaussian field can be obtained by taking the limit of the exponential…
Gaussian Multiplicative Chaos (GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is Gaussian field on $\mathbb R^d$ (or an open subset of it) whose correlation function is of the form $ K(x,y)= \log…
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
We discuss a Gaussian multiplicative chaos (GMC) structure underlying a family of random measures $\mathbf{M}_r$, indexed by $r\in\mathbb{R}$, on a space $\Gamma$ of directed pathways crossing a diamond fractal with Hausdorff dimension two.…
Let $B = (B_t)_{t \in {\bf R}}$ be a symmetric Brownian motion, i.e. $(B_t)_{t \in {\bf R}_+}$ and $(B_{-t})_{t \in {\bf R}_+}$ are independent Brownian motions starting at $0$. Given $a \ge b>0$, we describe the law of the random set…
We investigate critical quantum metrology,that is the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any…
Denote by $\mu_\beta="\exp(\beta X)"$ the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field $X$ on a domain $U\subset\mathbb{R}^d$. The case $\beta\in\mathbb{R}$ has been studied quite intensively, and…
The triangular elliptic operators are natural extensions of the elliptic deformation of circular operators. We obtain a Brown measure formula for the sum of a triangular elliptic operator $g_{_{\alpha, \beta, \gamma}}$ with a random…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
We study a model of $n$ one-dimensional non-intersecting Brownian motions with two prescribed starting points at time $t=0$ and two prescribed ending points at time $t=1$ in a critical regime where the paths fill two tangent ellipses in the…
We show that for $\gamma<\sqrt{4/3}$, it is possible to define the Levy area of a planar Brownian motion with the Liouville measure of intermittency parameter $\gamma$ as the underlying area measure. We also consider the case of smoother…
We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents $\gamma$ and $\nu$ -- depending on the polymer topology, on the dimension of the…
Through chaos decomposition we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.
The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical…
We compute the Brown measure of $x_{0}+i\sigma_{t}$, where $\sigma_{t}$ is a free semicircular Brownian motion and $x_{0}$ is a freely independent self-adjoint element that is not a multiple of the identity. The Brown measure is supported…
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The study of these martingales with complex parameters is a rather…
We consider the Brown measure of the free circular Brownian motion, $\boldsymbol{a}+\sqrt{t}\boldsymbol{x}$, with an arbitrary initial condition $\boldsymbol{a}$, i.e. $\boldsymbol{a}$ is a general non-normal operator and $\boldsymbol{x}$…
The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…