# Questions tagged [statistical-physics]

The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.

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**1**answer

65 views

### Expected size of matchings in a cubic graph

Let $G$ be a random cubic graph on $n$ vertices. Let $M$ be the set of (not necessarily maximum) matchings of $G$. What is the expected size (i.e. number of edges) of an element of $M$?
In other ...

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**0**answers

25 views

### how to filter measurement noise out of a set of data [migrated]

I need to find the best way to filter white noise from a set of data $(x_0,y_0),...,(x_n,y_n)$, $n>1000$, where
$x:\text{ is a time variable}$
$y:\text{ is a physical quantity}$
The noise is ...

**5**

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**1**answer

172 views

### Switching oriented paths in a graph

Consider an oriented graph (e.g. a finite part of the standard grid with some random orientations).
Each minute the following operation takes place: we choose uniformly randomly an ordered pair $(A,B)...

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**1**answer

85 views

### Upper bound on the number of induced subgraphs of the square lattice with all degrees even

An induced subgraph of a graph $G$ is defined by a subset of vertices of $G$ together with all edges in $G$ that connect vertices from the chosen subset.
Consider now an $n\times m$ square lattice. ...

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**0**answers

31 views

### Vertical and horizontal percolation on heterogeneous honeycomb lattice

I have a regular honeycomb lattice where a bond in the unit cell aligns with $(1,0)$; call this the horizontal direction. Each horizontal bond in the lattice is open with probability $p$ and each "...

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**0**answers

58 views

### How to mathematically justify the “sampling” over only $100$ random matrices to estimate percolation thresholds?

As mentioned in the textbook "Introduction to Percolation Theory" (Chapter 4) by Stauffer et al., the variation of spanning cluster percolation probability $\Pi$ in a finite $L < \infty$ square ...

**5**

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**1**answer

151 views

### A counterexample for the Mean Ergodic Theorem in $L_\infty$

The so-called Mean Ergodic Theorem goes back to von Neumann for Hilbert spaces. Later on, versions of this result in reflexive Banach spaces have also appeared (see, e.g., the book by Krengel, Ergodic ...

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**3**answers

141 views

### Single quantum particle entropy

Consider a wave function of a single particle in free space, whose evolution is described by the (non-dimensional) linear Schrodinger equation $$i\psi _t (t,\underline{x}) + \Delta \psi=V(\underline{x}...

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161 views

### Is this “stretched eigenvector” studied? (If so, what are its properties?)

An eigenvector is defined by
$$
\lambda \mathbf{v} = A\mathbf{v}.\tag{1}
$$
But suppose I change this to
$$
\lambda \mathbf{v} = A\mathbf{v}^\alpha,\tag{2}
$$
for real $\alpha\ne 1$, where $\mathbf{v}^...

**5**

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**1**answer

107 views

### An extension of the Izergin-Korepin determinant to the eight-vertex model

In the six-vertex model, edges in a square lattice are oriented so that the in-degree of each vertex is exactly two. This gives six types of allowable vertices:
$$\begin{array}{cccccc}
\begin{...

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**1**answer

118 views

### Wasserstein distance to the set of Gaussians ; Boltzman dissipation rate

I am interested in the $2$-Wasserstein distance for probabilities over ${\mathbb R}^n$,
$$W_2(\mu,\nu)=\left(\inf\int_{{\mathbb R}^n\times{\mathbb R}^n}|w-v|^2\pi(v,w)\right)^{1/2}$$
where the infimum ...

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**0**answers

78 views

### How to calculate the exact probability $p$ at which maxima occurs in the curves in an infinite system?

I'm writing with respect to this paper: Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice
Here's a link to the PDF ...

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63 views

### Not exactly directed percolation

Is the following problem known/well-studies? I'm looking for references or a name that I can look up.
I start with $N$ cell, each one divides into two cells, each one of the new cells either dies ...

**4**

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**1**answer

325 views

### Critical Exponents for Island Mainland Transition (Percolation Theory)

I was looking at this paper “Islands in Sea” and “Lakes in Mainland” phases and related transitions simulated on a square lattice on Percolation theory. The concept of phase transition used here seems ...

**4**

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**1**answer

117 views

### an application of nth moment of Poisson distribution with stirling number

I was reading the paper on arixv.
I was confused the equation of nth moment of Poisson distribution.
The detail and partial paper as follow:
...
For large N, this connection probability takes ...