Questions tagged [simulation]

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From biased coins (and nothing else) to biased coins

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
Peter O.'s user avatar
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11 votes
3 answers
2k views

On mathematical studies of the Mpemba effect

Since the days of Aristotle and Descartes, it has been known that under certain circumstances warm water freezes faster than cold water. This effect is now commonly known as the Mpemba effect, named ...
UwF's user avatar
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10 votes
1 answer
915 views

exactly simulating a random walk from infinity

In diffusion-limited aggregation on the square lattice, one lets a particle do "random walk from infinity" until it hits the current aggregate, at which point the site occupied by the particle is ...
James Propp's user avatar
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8 votes
1 answer
1k views

What is the "Tangle" at the Heart of Quantum Simulation?

The following questions generalize and naturalize the question that was originally asked. Provisional answers largely due to Will Sawin are now included. As was discussed in the question originally ...
8 votes
1 answer
433 views

Potts model simulation

I was wondering what were the state-of-the-art methods to simulate low temperature configurations of Potts-like models that exhibit a discontinuous phase transition. For models with a continuous phase ...
Alekk's user avatar
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6 votes
1 answer
543 views

Is this a Brownian motion?

I am building a 2D stochastic process as follows. I start with a point $P_0=(0,0)$. Then $P_k=(X_k,Y_k)$ is defined as follows, for $k>0$: \begin{align} X_k & =X_{k-1}+R_k \cos(2\pi\theta_k) \\ ...
Vincent Granville's user avatar
6 votes
1 answer
232 views

Violating an order statistic inequality?

[Edit: for posterity, I'm adding two small comments to the code explaining how to fix it, in light of Iosef Pinelis' answer below. Look for "Should be:" to find the corrections.] Suppose we ...
Bill Bradley's user avatar
  • 3,809
6 votes
2 answers
417 views

how to sample a conditioned diffusion

there are several reasons why we could be interested in sampling conditioned diffusions: if we observed a diffusion at discrete time and want to do some kind of inference on the parameters of the ...
Alekk's user avatar
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5 votes
2 answers
2k views

Real world example of use of Monte Carlo method for high dimensional integrals

The Monte Carlo method for numerical integration is usually presented as a method invented to efficiently compute high dimensional integrals numerically. However, I haven't found any source which has ...
David's user avatar
  • 141
5 votes
1 answer
3k views

How can I generate the simulated time series

I am curious how one can generate simulated time series data. I found a list of simulated series here and a similar tool for stock market. What is the best way to generate domain specific time series ...
Abhishek Tiwari's user avatar
4 votes
1 answer
153 views

Intractability of an integral by deterministic numerical methods

Suppose $X_1,\ldots,X_n$ is an i.i.d. sample from a probability distribution with continuous c.d.f. $F.$ Let $F_n$ be the empirical c.d.f. $$ F_n(x) = \frac 1 n \sum_{k=1}^n \mathbf 1_{X_n\le x} = \...
Michael Hardy's user avatar
4 votes
1 answer
147 views

How to simulate the fractional noncentral Wishart distribution?

I already asked this question on math.stackexchange but got no answer. For a non-integer number of degrees of freedom $\nu > p-1$, one can simulate the central Wishart distribution $W_p(\nu, \...
Stéphane Laurent's user avatar
4 votes
1 answer
659 views

How to draw a random normal matrix?

I would like to pick a random real normal (i.e. commuting with its transpose) matrix and I wonder if it can be done easily. I thought whether it would be possible to use a similar trick to drawing a ...
Domin's user avatar
  • 43
4 votes
0 answers
225 views

From biased coins to biased coins, as efficiently as possible

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
Peter O.'s user avatar
  • 637
4 votes
0 answers
106 views

Designing Character Other Than Temperature for Simulated Annealing on Combinatorial Optimization

Many research on designing temperature for simulated annealing is carried out. We wonder if there is any research on designing general feature of the Hamiltonian used in Simulated Annealing. For ...
Jiayi Liu's user avatar
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4 votes
0 answers
728 views

Monte Carlo sampling high dimensions with the halton sequence?

Referring to the Halton Sequence, Swiler et al 2006 state that In cases where a large number of input variables are sampled, Robinson and Atcitty recommend using a leaped sequence, where the ...
David LeBauer's user avatar
3 votes
2 answers
717 views

Is it possible to reliably generate a particular approximation of an ideal knot via a simulated annealing approach?

Say I take a cord, tie a loose knot in three-dimensional space, and pull tightly on the ends to generate an approximation of an ideal knot. If the cord has a fixed knot topology and a random initial ...
UltraBlue06's user avatar
3 votes
1 answer
160 views

What is the minimum and the maximum perimeter of a triangle with area $x$ that can be inscribed in a circle?

This question was posted in MSE but is still open hence posting in MO. The area of the largest triangle that can be inscribed in a circle of raidus $1$ is $\displaystyle \frac{3 \sqrt{3}}{4}$ for a ...
Nilotpal Kanti Sinha's user avatar
3 votes
2 answers
164 views

Drawing random variates from a partially described probability distribution

I have a probability distribution over $\{0,1\}^n$ but instead of knowing the full joint distribution $p(x_1,\dots,x_n)$, I only know $p(x_i=x_j)$ for each $i,j$. How could I draw a random binary ...
egosphere's user avatar
  • 163
3 votes
1 answer
85 views

Finite differencing scheme for Hamilton's equation with planar linkages

I am trying to simulate the movement of a planar linkage in the plane whose position and momentum obey Hamilton's equations, which is to say that $${{dq}\over{dt}} = {{dH}\over{dp}}$$ and $${{dp}\...
Charles Baker's user avatar
3 votes
1 answer
820 views

Sampling from a particular multivariate probability distribution

Given $3$ real variables $x_1, x_2, x_3 \equiv \bf{x}$, consider their probability density function (PDF) \begin{equation} P({\bf x}) = C \, p(x_1) \cdots p(x_3) \exp[f({\bf x})], \end{equation} where ...
James's user avatar
  • 333
3 votes
0 answers
355 views

A conjecture on consistent monotone sequences of polynomials in Bernstein form

A Conjecture In the following, a polynomial $P(x)$ is written in Bernstein form of degree $n$ if it is written as— $$P(x)=\sum_{k=0}^n a_k {n \choose k} x^k (1-x)^{n-k},$$ where $a_0, ..., a_n$ are ...
Peter O.'s user avatar
  • 637
2 votes
1 answer
145 views

How far away is $\max_{x: x \in \{0, \ldots, N\}} |W(x/N)|$ from $\max_{0 \leq t \leq 1} |W(t)|$ ($W(t)$ a Wiener process)?

How far away is $$\max_{x: x \in \{0, \ldots, N\}} \left|W\left(\frac{x}{N}\right)\right|$$ from $$\max_{0 \leq t \leq 1} |W(t)|$$ In other words, if you simulate a Wiener process over a finite ...
cgmil's user avatar
  • 235
2 votes
1 answer
463 views

Multiple Wiener-Ito integral distribution

Distribution of standard Ito integral is well known: $$I_1(f) = \int_0^T f(t)dB(t) \sim \mathcal{N}\bigg(0, \int_0^T f^2(t)dt\bigg).$$ Is it possible to find the distribution of multiple Wiener-Ito ...
Aleksandr Samarin's user avatar
2 votes
1 answer
2k views

Design a Galton Board to simulate a uniform distribution

This link http://mathworld.wolfram.com/GaltonBoard.html suggests that a certain specific placement of pegs can be used to simulate a binomial or a normal distribution. Is there a specific peg ...
vkmv's user avatar
  • 121
2 votes
0 answers
37 views

Discrete approximation of continuous determinantal point processes

(throughout, "DPP" denotes "Determinantal Point Process") TL;DR: Discrete DPPs are straightforward to compute with, continuous DPPs less so. Can we approximate continuous DPPs well ...
πr8's user avatar
  • 688
2 votes
0 answers
126 views

Multiple Wiener integral as Witt polynomial of Brownian motion

I know that if i have a Brownian motion $W_t$ the multiple Wiener integral $\int_0^t \int_0^{\xi_1}...\int_0^{\xi_n} dW_{\xi_1}...dW_{\xi_n}$ can be expressed as $H_n(\int_0^t dW_s)$ where $H_n$ is ...
Marco's user avatar
  • 263
2 votes
0 answers
514 views

Convergence Based on Recurrence Relation

I am studying a sequence based on the following recurrence: $$X[t] = \sqrt{\alpha X[t-1]^2+(X[t-1]^2-\alpha X[t-2]^2)\frac{(2-X[t-1])^2}{X[t-1]^2}}$$ $$X[0]=0$$ $$X[1]>0$$ $$\alpha \in (0,1)$$ I ...
Stefan Postavaru's user avatar
2 votes
0 answers
53 views

brownian motion of 100 nm spherical particles in evenly spaced arrays [closed]

Generally looking for perspective from the computational experts. Question comes down to how tractable is the following problem. Let's say at time 0, I have a 2-D array of $N = 10$ spherical particles ...
Pau Harmon's user avatar
2 votes
0 answers
89 views

Customers and Anti-Customer Queueing Problem: What is the Customer delete probability

Hello may I ask for your help? First the setting: I have got a problem with some queueing theory. The whole problem would be a grid of nodes, all nodes have an operation intensity $\mu_{i,j}$. ...
xpnerd's user avatar
  • 21
2 votes
0 answers
153 views

A question on discrete numerical simulation on fluids mechanics

I read the paper "Stable, circulation-preseving simplicial fuids" by Elcott, et al: http://www.cs.jhu.edu/~misha/Fall09/Elcott07.pdf. It gives a structure preseving discretization of fluids. I have ...
Hao's user avatar
  • 21
1 vote
4 answers
3k views

Will a random walk on [0, inf) tend to infinity? [closed]

Consider a random walk on [0, inf) where you start at 0. With probability p = 0.5, you increase by 1. With probability (1-p) = 0.5, you decrease by 1, but not below 0. As time goes to infinity, will ...
wjomlex's user avatar
  • 503
1 vote
2 answers
105 views

Another question on provable non-existence of an efficient deterministic numerical method

Herewith I submit what may or may not be considered a simpler version of this question. The question is whether it is provable that there is no efficient deterministic numerical method for a ...
Michael Hardy's user avatar
1 vote
1 answer
181 views

Sampling uniformly in a ball of radius $\epsilon$ in the space of dicrete r.v. of m modalities for the total variation metric

I am looking for some reference or an algorithm that allows to sample uniformly in the ball centered at a discrete random variable of n modalities in the TV distance. For the record for 2 discrete ...
The Bridge's user avatar
  • 1,304
1 vote
1 answer
353 views

[Numerical Mathemtics] How to solve hexagonal central differences

I want to simulate a 2d linear wave equation on a circle ($\displaystyle\frac{\partial^2 z(x,y,t)}{\partial t^2}=v^2\cdot\left(\displaystyle\frac{\partial^2 z(x,y,t)}{\partial x^2}+\displaystyle\frac{\...
willeM_ Van Onsem's user avatar
1 vote
1 answer
2k views

Monte Carlo sampling from correlated empirical distributions

I have a dataset that contains six correlated variables, and I want to sample new data so that each variable has the same marginal distribution as the original data, and the correlations are also the ...
David's user avatar
  • 11
1 vote
1 answer
92 views

Choose uniformly from fixed-length paths in $[0,n]\cap\mathbb{Z}$ with fixed start and end

Let $X_k$ be a symmetric (discrete time) random walk on $\mathbb{Z}$ and let $m,n\in\mathbb{N}$. I want to chose uniformly from the paths of $X_k$, which start at $0$ stay in $[0,n]\cap\mathbb{Z}$ ...
Ikaros's user avatar
  • 113
1 vote
1 answer
295 views

Condition Number and CFL Condition in Finite difference Methods [closed]

when applying a Finite Difference scheme for an IVP, two factors come to mind when considering stability: One factor would be the condition number of the approximation operator. The other factor ...
Amir Sagiv's user avatar
  • 3,544
1 vote
1 answer
147 views

Staggered timing on 2-D random walks by multiple agents

In 2-D lattice random walks by multiple drunks who can't step onto each other, mathematically I would just say the whole cellular automaton updates "at once". But to simulate this on a computer, I ...
isomorphismes's user avatar
1 vote
0 answers
77 views

Conditioned random walk over a graph

I want to solve for a conditioned random walk over a graph. I have a directed graph $G$. The random walkers start at a fixed node, Source. They all need to end up at fixed node, Sink. So the random ...
highBandWidth's user avatar
1 vote
0 answers
40 views

Langevin dynamics or stochastic gradient flow for grand canonical ensemble

We know that for a measure exp(-U(X)) (canonical ensemble), we can use the dynamic dX=-DU(X)+ noise to sample the measure as t goes to infinity. Is there any dynamic corresponding to the grand ...
Hausdorff's user avatar
1 vote
1 answer
71 views

What new fractional brownian motion (fBm) simulation methods have emerged since 2010? [closed]

I want to describe new methods for simulating fBm, as in the work of Coerjolly and Dieker, but new methods are not very easy to find.
PlaDJ's user avatar
  • 11
1 vote
0 answers
77 views

Real life applications of distributions through models or simulations [closed]

What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test ...
Lateef's user avatar
  • 91
1 vote
0 answers
165 views

A mathematical biology reference request

Is there any mathematical articles that describe the differential equation modelling of locomotion of amoeba using pseduopodia? I am looking for physics based models of pressure difference modeling of ...
Turbo's user avatar
  • 13.7k
1 vote
0 answers
115 views

Monte Carlo Simulation - efficient simulation of tail outcomes [closed]

When running Monte Carlo type simulations in situations where you're only interested in tail outcomes, do you know of a way to only simulate those outcomes, so that you can come up with more reliable ...
aayush anand's user avatar
1 vote
0 answers
88 views

Importance sampling for bernoulli-sequence, favouring long sequences of ones

Assume we have a sequence of i.i.d. bernoulli-distributed random variables of length $n$. I'm interested in doing rare event simulation and my event depends, among other random factors, on the ...
user2426460's user avatar
1 vote
0 answers
505 views

9-point stencil "equivalent" for advection equation [closed]

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
mathdummy's user avatar
  • 111
0 votes
1 answer
695 views

Generating random variables from the Cantor Distribution [closed]

I am looking for a method (exact, if possible, but at least asymptotically correct) for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In ...
user avatar
0 votes
1 answer
200 views

How are epidemic models simulated in case of mobility?

I am not a mathematician but out of curiosity I am trying to implement the SIS epidemic model when the nodes have mobility to understand how it will change the results. I understand how to perform ...
Legend's user avatar
  • 429
0 votes
1 answer
68 views

Simulation of multivariate logistic distribution conditional to a plane

For an algorithm, I have to simulate $X_1, \ldots, X_n \sim_{\text{iid}} \text{Logistic}(0,1)$ conditionally to the event $(X_1, \ldots, X_n) \in P$, where $P$ is an affine plane in $\mathbb{R}^n$. I ...
Stéphane Laurent's user avatar